Never had a problem with bringing about the alliance, but I've always done all the quests (except destroy the other ship) for both sides.
Typically I do them in tandem. Get the flag quest, visit Umpani base, buy flag, sign up with Umpani, do obstacle course. Go back to Z'ant, give flag, get Raven quest, go up and kill him. Then back to Umpani, present T'rang arm.
For the moliri, I give the Mook the Umpani offer. However, that's okay, since you can just show the moliri to Z'ant and he's happy.
Of course, all that comes to a halt when each side wants the other's mother ship destroyed. I don't do either of those.
Then after the rescue at the Away Camp, I go see Z'ant first. He's a little testy at first, but Drazic and Rodan convince him. Then we go to Yamir.
I've never tried to do the alliance just working for one side. And, of course, I keep far away from He'Li, who knows too much
Nightowl2