Not sure how to reply to you Trivin, I am a newbie at the game, so my experience is rather severely limited. When I play and I find two of my allies at odds, I side with one and take the loss of influence or good relations from the other.
Then I try to see what I can do to 'up' the good relations again, like a mission or giving a ability or something like that.
It becomes a sort of roller coaster for me, losing influence here and winning there, then losing where I won and winning again where I lost.
It takes a while and is sort of like a slow dance to get relations as high as I can across the board.
But it doesn't always work out good for me. And sometimes I have to try to sacrifice one to boost the other, and losing an ally in the process.
Mid to late gate has been a killer for me usually as one of the 'Empires' forms and I wind up losing the game, so I am not sure my suggestions on strategy will be good overall for you. But if you can do the balancing thing, and not have to lose one permanently you might be in a better position when the 'Empire' forms and have a better chance at winning the game.
At least I hope you will, take care,
-Teal