Belshazzar was for many years held by liberals as an example of the Bible in error. There is no doubt that the exact relationship of Belshazzar and Nebuchadnezzar is a matter of debate, even among conservative theologians. However I believe that by careful reconciliation of the better commentators and close attention to the role of the queen it is possible to produce a viable family tree that will show the Bible to have been right all along. Understanding that tree may also give us some insight into why Belshazzar made the mistakes he did.
Jamieson-Fausset-Brown makes Belshazzar to be the son of Evil-Merodach, the son of Nebuchadnezzar. Neriglissar murdered Evil-Merodach his brother in law and took the throne. Following him his son reigned but 9 months and was then replaced by a people's choice of Nabonidius. Under this scheme Belshazzar was tolerated to be a sub-ordinate king in deference to the fact that he was actually of the royal line whilst Nabonidius wasn't. This also explains why the Babylonian account allows for an honorable surrender of the principle king in Borsippa rather than recording the humiliating loss of Babylon.
JFB is rather less concrete in the identification of 'the queen', making her the wife of either Nebuchadnezzar himself or Evil-Merodach.
Adam Clarke takes a similar line on Belshazzar himself, making him the son of Evil-Merodach. Clarke however ignores Nabonidius and dismisses Neriglissar and Laborosoarchod as satraps. He does give an interesting clue about the queen however pointing out that she may have been Amiyt the wife of Nebuchadnezzar but that she may have been Nitocris.
Nitocris is also the name suggested by JFB who adds the information that she completed many of the works started by Nebuchadnezzar and that Herodotus credited them to her. Clarke points out that she was credited with great wisdom and that she was chief of public affairs. He also suggests that she may have been the mother of Belshazzar.
Looking at the biblical account we notice a few features of her, she was well acquainted with Nebuchadnezzar, that she could talk to the king without invite and that she was listened to. It is interesting too that the Bible introduces the queen simply as 'the queen' as if that description alone would be enough to make clear who was being referred to.
It is however two entries in Easton's Bible dictionary that begin to unpick the puzzle. First in the entry to Nergal-Sharezer we are told he was married to Nebuchadnezzar's daughter, but we are also told that Nabonadius had a son Belshazzar. Then in the entry on Belshazzar we find he is the son of Nabonadius by Nitocris widow of Nergal-Sharezer.
By gluing these accounts together and centering around the queen I think we have a probable course of events.
Nebuchadnezzar dies, Evil-Merodach comes to the throne. The husband of Nitocris (the daughter of Nebuchadnezzar) usurps the throne using his wife to establish legitimacy. The people would have known her, if she were as effective as contemporary accounts suggest; they would have liked her. Nergal-Sharezer dies and is replaced by their son. However the son is too young to be credible, a populist Nabonidius begins to look like a threat. The queen mum swings into to action and marries Nabonidius, securing her position and giving him a legitimate claim to the throne. But a deal is struck; Belshazzar is to be king.
It is even possible that Belshazzar was an adopted son of Nabonidius and that he really pertained to the queen's previous marriage, after all Nabonidius only reigned 17 years which is not a long time to produce a son old enough to have wives and concubines. It is interesting too that Nabonidius stayed outside of Babylon, it is almost as if he got the rest of the empire in return for the queen and her son getting the capital itself.
If the above is true then it explains the biblical account perfectly. The queen would have been extremely important, a key figure throughout at least 3 reigns and would have had a detailed knowledge of her father. It also explains why Belshazzar could only offer the third place in the kingdom: he himself had the second.
Possibly this course of events could also explain how Daniel got sidelined. As a favored advisor of Nebuchadnezzar it is not hard to imagine at least one of the non-royal kings considering him a threat, it is also not impossible to imagine the queen having been smart enough to keep him around to provide the advice she needed. It is interesting that whilst Daniel was clearly disturbed at the thought of Nebuchadnezzar's downfall he didn't seem to have such loyalty to the monarchy by the time of Belshazzar.
It may also explain the behavior of Belshazzar that led to his downfall. You can imagine that while she endured two men as husbands that were not of royal descent she would have kept telling her son that he was special. He was the real heir to the throne. In fact this may account for her describing Nebuchadnezzar as the father of Belshazzar, she had been raising him as a direct heir.
Certainly in Belshazzar we see a man who appeared to think he was untouchable. He had been defeated in battle two years earlier and had had to retreat into Babylon. Surrounded by tremendous defenses and with twenty years supply of food he felt able to ignore the enemy without.
The thought that he was under siege puts into context his extravagance in throwing a feast for a thousand men. In fact doing that was somewhat undignified for an eastern potentate and bringing in the wives and concubines was very much out of form as seen by Vashti's refusal to a similar invitation.
The human explanation for this behavior that lead to his downfall is given in v1; he had drunk before them. In fact wine drinking is referred to three times in four verses, which suggest excess. Beautifully this same fact points to the real explanation of his downfall which is given in Jer 51:39 "In their heat I will make their feasts, and I will make them drunken, that they may rejoice, and sleep a perpetual sleep, and not wake, saith the LORD." We have already seen that Babylon was only going to survive through three generations; here we see how it is going to fall. Verse 57 of the same chapter is more specific naming many of the fighting men as taking part in the drunkenness. It is very possible that Belshazzar had rendered all of his senior officers drunk at the same time. This mistake is particularly reprehensible when you consider that the Assyrian empire had fallen after a similar error.
However foolish that may have been worse was to come. Much as Nebuchadnezzar attempted to defy the silver part of the image we see Belshazzar attempting to defy God. He took the plate his grandfather had taken from Jerusalem and defiled it. This could be seen as mere revelry but it is significant that the Bible goes on to say that he praised the gods of gold, silver, iron, brass and stone. This suggests he knew full well he was defying the God of the Hebrews.
With the consequences of his actions inevitable we are left to history to provide the precise details of the destruction. Adam Clarke holds that the feast was in honor of Sheshach in which case Darius would have been aware that this was a great feast day. He took the opportunity to divert the Euphrates, which thus drained the huge moat surrounding Babylon. Further, the river ran through the middle of Babylon so it is possible that draining it actually opened up a tunnel under the walls right into the center of Babylon. Either way, Darius now had the advantage of night cover, surprise and a defending army without competent leadership. Prophecy was fulfilled. The time of the gentiles moved into its silver phase.
I believe that in the above I have shown the handiwork of a successful, intelligent, scheming woman. We have also traced the mistakes of a self-indulgent, overly confident young man. But what we have really seen is that throughout it all and despite them all the will of God is done. It obviously wasn't written at that time but Galations 6:7 is undoubtedly the lesson to be learnt --
Be not deceived; God is not mocked: for whatsoever a man soweth, that shall he also reap.