The entire Khangates of the Mongolian empire recruited soldiers and resources of conquered states. Of course these soldiers at most times were recruited against their will. Is it the threat of the slaughter of kindred that essentially forces these soldiers into the ruling army? Taking into account, the language barrier, different religious affiliations and obvious cultural differences, will cohesiveness of such an army be possible? If so, how exactly is it done? Kublai Khan's army experienced this problem, with the Chinese and Korean armies amalgamated into his. Perhaps this was the reason for his inability to conquer Japan (other factors too contributed).
In historical practice this varied widely. It really depends on so much going on in the world at that time, what the societies look like, how big the armies are, etc. Here are just two examples of how this could work in your story:
To face a larger threat
Philip II of Macedon had quire remarkable victory at the Battle of Chaeronea, which wiped out most of the fighting forces of Thebes and Athens. He had basically conquered the main fighting force of the Greek city states, and had he marched through Greece, he undoubtedly would have wiped through the country. However, Philip didn't go to Greece to conquer it - he wanted Greece on his side so (a) he didn't have to worry about them while fighting Persia, and (b) he could use their forces to fight Persia. After this decisive battle, the League of Corinth was set up, effectively unifying all Greece (sans Sparta) under Philip as a hegemony (which, from a military perspective, basically made them a puppet state of Macedon). All the remaining fighting forces of Greece were essentially recruited into the Macedonian army, under Philip's authority. The advantage to the soldiers was:
- They won't die fighting Macedon, which would have been the near-guaranteed outcome
- Their home city-states can maintain some sense of independence from Macedon (their own taxes, laws, etc) instead of being subjugated entirely.
- By helping Philip fight Persia, they can might be able to liberate captured city-states from Persia and help re-instate trade routes
- Prevent Persia from conquering Macedon, as Persia was clearly set on conquering everyone and Philip was at least nice enough to give them some independence. The enemy of my enemy is my friend, I guess.
- Gain victory and glory by fighting the great evil that is Persia
To gain wealth or social status
Most ancient societies had some type of cast system. Even if it was not strictly defined, movement from rich to poor was difficult if not impossible. The Romans had a weird system where the wealthy were encouraged to be "patrons" (coming from "pater" which means "father") - a type of social father, so to speak - by being generous and giving to the arts, to the poor, etc. But land was held and owned by the wealthy alone.
All resource comes from the land. Food, mining, wood, etc. A Roman citizen with little or no land would have no way to gain land by any economic means. It happened, but so very rarely. Land is precious. Land is wealth. Roman soldiers were often promised their base wages (most numbers put this around 225 denarii a year, but it fluctuated), but on successful conquest or retirement they were also promised land - and with that land a lump some of money (as a "veteran benefit" - usually for soldiers were were around 25/30 years). This would give the soldier - and their families - the only realistic path forward out of their social class, and to gain wealth.
Now, Rome only allowed Roman citizens to join the army (they even had to pay for their own military gear!), but there were times (eg, Julius Caesar in Gaul) where their army was not big enough. As Julius was stomping around Gaul, invading, conquering, killing, pillaging, there were a few times where he did recruit Gauls to help him fight. A noticeable example was with Vercingetorix, where Caesar used some Gallic troops, promising them a portion of spoils, or land, or whatever to (a) get them to stop annoying him, and (b) put down Vercingetorix. Granted, Caesar often put these troops in vulnerable positions to kill them off, or cheated them on the payout.
But think from the perspective of the Gallic troops: they're already conquered, and provoking Caesar means he just kills them all. They've lost a lot of land and resources fighting him, and now they lost the war. If they recruit in and fight for Caesar, then they can move from poor to rich. If they don't, Caesar will eventually take Gaul anyway. Why not help him and get your only chance and moving up in the world?
From the perspective of an individual soldier in an ancient army, there's really no difference before and after the amalgamation. Regiments will continue to be raised primarily from one part of the empire: say, three from Alicevania, two from Bobtopia, one from Evopolis. If you're a Bobtopian slinger, you serve in a regiment that is almost if not entirely Bobtopian in origin. There may be a few Alicevanians in the general's coterie, but that's none of your business, and it's not something you'll have to deal with on a day-to-day basis. On the battlefield, your officers tell you where to maneuver and who to attack, and (usually) that's the end of it. There's no incoherence on account of cultural, language, religious, or other difference because you're kept separate from each other.
Of course, ancient armies tended to be rather draconian and armies in general don't love deserters, but there's no special threat needed to compel you to fight. You fight for the same reason that you always did: because the king or whoever tells you to. The king might be doing so at the behest of another king, or indeed an emperor, but that's not your concern. Your concern is to finish your time and go home with a big bag full of plunder (or a tax exemption, or citizenship for your family, or some other reward). The idea of nationalism and the inalienable sovereignty of the state being important to the common people is far in the future.
As for the people whose business this is, well, they have their own reasons for capitulating. Presumably they were either uninterested in fighting the empire or were defeated, and that situation hasn't changed. They will have to cooperate with their new rulers, and there are some logistical hurdles there (languages being an obvious example) - but this is on the scale of a few dozen people. These issues can be sorted out.
Note that although this will minimize the impact of differences between parts of your empire, it won't do anything about animosity between them. The British Empire, for instance, had occasional issues when deploying regiments side by side that came from historically opposing groups - like Scots and Irishmen, or Scots and English, or Scots and other Scots. Commanders would have to consider the temperaments of the individual units and how they were likely to interact when deciding on an order of battle.
Is it the threat of the slaughter of kindred that essentially forces these soldiers into the ruling army?
That's a possible reason, but the overriding one is that they are soldiers, no work, no pay, they'll starve to death.
So either they just work for a new employer who has been proven to be successful and might make them wealthy, or they run away and grub around in the dirt trying to make a living in constant danger of being killed.
Of course these soldiers at most times were recruited against their will.
Quite often these soldiers were recruited against their will by their own leaders as well, the lower ranks anyway.
The soliders might not have any concept of nation, or who the boss of the boss of the boss of the village headman is. Look at European history -- often the court of the king spoke a different language than the peasantry.
There is religion, and there is a social order, and the potential soldiers are at the bottom of the order and people on top tell them what to do.
The development of a nation (and of a flag larger numbers of people would fight and die for) came much later.