Both chapters relate to Nebuchadnezzar’s dreams but there’s a different reason to unite them. The case is that the interpretation of chapter 4 was written much later – in March 2018. And not to interfere with the sequence, the interpretations of chapters two and four were united in one journal article.
 
The Book of Daniel, chapter 2
The second chapter needs almost no interpretation. God provides Daniel with an exhaustive explanation of Nebuchadnezzar’s dream. Responding to the king’s thoughts, God shows him what will happen in the future: “To you, O king, as you lay in bed, came thoughts of what would be hereafter, and the revealer of mysteries disclosed to you what is to be.” (Dan.2:29). It should be noted that this dream covers the entire history of humankind to the very end: “but there is a God in heaven who reveals mysteries and he has disclosed to King Nebuchadnezzar what will happen at the end of days.” (Dan.2:28).
Five kingdoms are described here, which are the five world empires, including the first Babylonian kingdom, which refers not only to Babylon, but also to Persia, Assyria, Egypt and perhaps, even the kingdom of Israel in king Solomon’s times. Wherever the central government was located at every moment of the history of the Babylonian kingdom, the Middle East remained a single political and cultural space. The fact that it’s the world empires that are mentioned here is supported by the words: “You, O king, the king of kings – to whom the God of heaven has given the kingdom, the power, the might, and the glory, into whose hand he has given human beings, wherever they live, the wild animals of the field, and the birds of the air, and whom he has established as ruler over them all – you are the head of gold. After you shall arise another kingdom inferior to yours, and yet a third kingdom of bronze, which shall rule over the whole earth.”(Dan.2:37:39).
In most other prophecies, but for Dan.8, the Babylonian kingdom is omitted, because they talk about what is coming, but not about what there is now and will remain in the future. Surprisingly, but each subsequent kingdom existed for about half of the previous one’s term.
The Babylonian kingdom, represented by the golden idol’s head, ruled the world for 1598 years (XIX century BC — 202 BC). 
The Roman Empire, which the dream shows are the chest of the idol with its hands made of silver — 772 years (202 BC — the victory of Rome in the Second Punic War and 550 — the period of the greatest territorial expansion of the Byzantine Empire after the conquests of Justinian I). 
The Mongol Empire shown as the belly of the idol with bronze hips — 382 years (1203 — reforms that laid the basis of the Mongol Empire, and 1585 — the fall of the Timurids, maybe later).
The European Empire shown as the idol’s iron legs — 200 years (1698 — the beginning of Peter I’s reforms, 1897 — the USA abandoned the Monroe doctrine).
The Contemporary Empire shown as the idol’s legs, partly iron, partly clay — 127 years (1897-2023). 
Probably, it is the decreasing time of dominating the world that explains that the material for each part of the idol becomes cheaper and cheaper.
Dan.2:43 tells us of the last kingdom: “As you saw the iron mixed with clay, so will they mix with one another in marriage, but they will not hold together, just as iron does not mix with clay.” The iron here is the states that used to be a part of the fourth iron kingdom, i.e. of the European Empire: England, Germany, France and Russia, as well as these countries’ ethnic groups that laid the basis of the US power. And the clay refers to the “clay pots” from Rev.2:26-28, which describes the colonial conquest of the countries of America, Africa and Asia by European peoples during the Fourth Church in Thyateira (1370–1648): “To everyone who conquers and continues to do my works to the end, I will give authority over the nations; to rule them with an iron rod, as when clay pots are shattered — even as I also received authority from my Father. To the one who conquers I will also give the morning star.”
The words “they will mix with one another in marriage” mean that while maintaining, albeit partial, the dominance of the European Empire states, associated with iron, the national composition of these states will significantly change due to migration and the slave trade. And the words “but they will not hold together, just as iron does not mix with clay” – mean that migration will not have any significant impact on the metropolises’ policy towards the colonies. 
As we can see, just as in the Revelation of John the Divine, the mountain here means a state or a kingdom: “As you looked on, a stone was cut out, not by human hands, and it struck the statue on its feet of iron and clay and broke them in pieces. Then the iron, the clay, the bronze, the silver, and the gold, were all broken in pieces and became like the chaff of the summer threshing floors; and the wind carried them away, so that not a trace of them could be found. But the stone that struck the statue became a great mountain and filled the whole earth.” (Dan2:34-35). But this Kingdom is not from this world: “And in the days of those kings the God of heaven will set up a kingdom that shall never be destroyed, nor shall this kingdom be left to another people. It shall crush all these kingdoms and bring them to an end, and it shall stand forever; just as you saw that a stone was cut from the mountain not by hands, and that it crushed the iron, the bronze, the clay, the silver, and the gold.” (Dan.2:44-45).

The Book of Daniel, chapter 4
The approximate time of the dream is 568 BC.
It describes Nebuchadnezzar’s dream, in which he is warned not to be carried away by his thoughts about the power of the Babylonian kingdom and the beauty of Babylon, since Nebuchadnezzar has almost nothing to do with them: “At the end of twelve months he was walking on the roof of the royal palace of Babylon, and the king said, “Is this not magnificent Babylon, which I have built as a royal capital by my mighty power and for my glorious majesty?” While the words were still in the king's mouth, a voice came from heaven: “O King Nebuchadnezzar, to you it is declared: The kingdom has departed from you! You shall be driven away from human society, and your dwelling shall be with the animals of the field. You shall be made to eat grass like oxen, and seven times shall pass over you, until you have learned that the Most High has sovereignty over the kingdom of mortals and gives it to whom he will.” (Dan.4:29-32).
The “tree” here refers to the Babylonian kingdom: “Upon my bed this is what I saw; there was a tree at the center of the earth, and its height was great. Tree grew great and strong, its top reached to heaven, and it was visible to the ends of the whole earth.” (Dan.4:10-11).
The “main stump” is Babylon as the capital of the Babylonian Kingdom: “He cried aloud and said: ‘Cut down the tree and chop off its branches, strip off its foliage and scatter its fruit. Let the animals flee from beneath it and the birds from its branches. But leave its stump and roots in the ground, with a band of iron and bronze, in the tender grass of the field. Let him be bathed with the dew of heaven. And let his lot be with the animals of the field in the grass of the earth.” (Dan.4:14-15).
The words “And let his lot be with the animals of the field in the grass of the earth” and simultaneous order to “let the animals flee from beneath it and the birds from its branches” should be understood as Babylon being ruled by all four future world empires, which are shown as beasts in Dan.7.
“A band of iron and bronze” — is the subjection of Babylon primarily to two of these beasts: the European Empire shown in Dan.2 as the iron legs of the idol, and the Mongol Empire shown as the belly of the idol and its bronze hips.
Dan.4:16 promises to Babylon: “Let his mind be changed from that of a human, and let the mind of an animal be given to him. And let seven times pass over him.” The words “let his mind be changed from that of a human” may probably mean that Babylon will never be Christian. For comparison, we can quote the words from Dan.7:4 that describe the Roman Empire: “The first was like a lion and had eagles' wings. Then, as I watched, its wings were plucked off, and it was lifted up from the ground and made to stand on two feet like a human being; and a human mind was given to it.” The two wings are the Western and the Eastern Roman Empires; each of them has its rulers – “feathers” similar to the ones in Ezr.3. Both of them fell but adopted Christianity, as imply the words “a human mind was given to it.”
The words “and let seven times pass over him” should be, on the one hand, understood as the fullness of time, that is as the fact that this fate will befall Babylon before the time ends. On the other hand, as seven years, or 365.25 x 7 = 2,556.75 years, which the prophecy about Babylon’s loss of its status of the Babylonian kingdom’s capital covers. Indeed, the Persian king Cyrus II died in 530 BC. He conquered Babylon and was seen as the ruler of Babylon and the liberator of the peoples forcibly brough to Mesopotamia by the Babylonian kings. From that time, Babylonia was no longer an independent kingdom but a satrapy of the Achaemenid Empire with the capital in the city of Pasargadae. It is unknown when exactly the capital was transferred from Babylon to Pasargadae. Cyrus the Great began to build his capital in 546 BC, but died before the construction was completed. Pasargadae becomes the capital only under Cyrus’ son – Cambyses II, that is between 530-522 BC. If we deduct 2030 from 2,556.75, then the resulting year – 526.75 – will be just the middle of this interval. 
The words “at the end of twelve months” (Dan.4:29) and “O King Nebuchadnezzar, to you it is declared: The kingdom has departed from you!” (Dan.4:31) should be understood as a prophecy about the future of the Babylonian kingdom but not Babylon. Twelve months here is 365.25 days or years, after which the Babylonian kingdom will give way to the Roman Empire as a hegemon. Indeed, if we deduct 365.25 years from the year of the dream – 568 BC – we will get 203-202 BC. It was in 202 BC that Rome won the Second Punic War, thus becoming the strongest state in the Mediterranean region. 

The interpretation given to Nebuchadnezzar by Daniel in Dan.4:20-26 does not contradict the one provided here: “The tree that you saw, which grew great and strong, so that its top reached to heaven and was visible to the end of the whole earth, whose foliage was beautiful and its fruit abundant, and which provided food for all, under which animals of the field lived, and in whose branches the birds of the air had nests—it is you, O king! You have grown great and strong. Your greatness has increased and reaches to heaven, and your sovereignty to the ends of the earth. And whereas the king saw a holy watcher coming down from heaven and saying, ‘Cut down the tree and destroy it, but leave its stump and roots in the ground, with a band of iron and bronze, in the grass of the field; and let him be bathed with the dew of heaven, and let his lot be with the animals of the field, until seven times pass over him’— this is the interpretation, O king, and it is a decree of the Most High that has come upon my lord the king: You shall be driven away from human society, and your dwelling shall be with the wild animals. You shall be made to eat grass like oxen, you shall be bathed with the dew of heaven, and seven times shall pass over you, until you have learned that the Most High has sovereignty over the kingdom of mortals, and gives it to whom he will. As it was commanded to leave the stump and roots of the tree, your kingdom shall be re-established for you from the time that you learn that Heaven is sovereign.”
The words “the tree… it is you, O king” can also refer to the Babylonian kingdom. And the words “it was commanded to leave the stump and roots of the tree, your kingdom shall be re-established for you from the time that you learn that Heaven is sovereign” may mean that Babylon will keep its borders (modern Iraq) until the coming of the Kingdom of God, i.e., until the end of times. 
Thus, neither Daniel’s interpretation nor the subsequent fulfillment of the dream exemplified by Nebuchadnezzar contradicts the interpretation offered here. However, as often the case in the prophetic books and the New Testament, the main meaning is hidden behind the secondary one.