Same thing happened with me, only it was for Gym's special missions.
Just do random extra, friendship, and free missions. When you get to the pre-battle screen, just check to see who your allies are. If it's not someone you want to gain trust with, then just exit back and re-enter till you get who you want. You allies and enemies are for the most part random. Even people who hate you can be set up as allies. The stages themselves are usually random as well.
That is what I'm doing all the time, mostly the first two friendship missions regarding characters that either detest or mistrust you. The problem is, nothing seems to happen. I heard that chances of gaining the trust of other pilots is increased if you save them from a tight spot, but the issue is, even on hard when it's just a stage where the objective is nothing more than clearing all fields, they usually never lose that much health and clear the fields on their own.
And charisma isn't doing the trick either. I guess I can check off Zeon in Kira's case, there's too many of them that don't like me, and as far as I recall the one to recruit you to Zeon has to be Dozle, and I kick his ass all the time. The only Zeon people who like me are Gyunei and Nagai, but I believe to get into Neo Zeon, it has to be Char, as Haman is for Axis.