Ok so I've heard that it's possible to make the umpani and the t'rang work together, but how can I achieve that?
The walkthroughs and stuff say that I have to do everything for both sides except for the last mission. My current situation is that Umpani ordered me to destroy the T'rang ship and the T'rang ordered me to destroy the Umpani ship. I'm not sure this is the best course of action if I want them to come to an agreement.
What do I do now?
I also have Astral dominae and Chaos moliri on me.

I'm not sure whether actually having either of those missions active will block the option, though completing either one certainly will.

To forge the alliance you'll need to become a Rapax templar and then visit the war camp that appears in the southeast. The timing of this is tricky, however - I don't remember the exact trigger points, but if you go too far in collecting the artifacts, the war camp will disappear and you won't be able to access it. (There probably would have been further plot events around the Rapax war effort at that point but development was cut short.) In the camp you may be able to help out a pair of prisoners, and with their assistance, get the T'rang and Umpani leaders to work together.

The trigger is having the items... Astral Dominae and Chaos Moliri

If you don't want the war camp just put one of them into a chest and return to the area.

Is it just those two, or any two of the three? (It has been years, but I'm pretty sure I had the war camp appear when I'd collected the Destinae and Moliri, but not the Dominae, when I played this at release.)

Maybe... of course you would have to get past a very BIG fish at low level.

The real start for the quest is to find Drazik and Rodan and bringing them to Z'Ant and Yamir. Breaking them out of their cages will trigger the start of the alliance quest if you are still friendly with each of them

WARNING: DO NOT PUT ANY ARTIFACTS INTO ANY CONTAINERS IN THE WAR CAMP!

If you put at least two of the three artifacts into containers, you will not be able to get the war camp to appear unless you retrieve at least one of them. If those containers were in the war camp, you will not be able to retrieve those items at all. This is gamebreaking, as it makes the game un-winnable. So as I said, do not use containers in the war camp to store artifacts.

If you want to store the artifacts, put them somewhere else, like in a locker in Arnika, that does not change.