Letting the AE win is not necessary a bad thing.
The awakened empire starts generating decadence - a big penalty to produced resources and fleet capacity - and speed it is generated is proportional to the size of the empire.
Decadence is effectively a meter, going from 0 to 100, that starts filling up for Awakened Empires once a certain amount of time has passed since awakening. The larger they are (both in terms of owned planets and subjugated empires), the faster it builds up. Decadence reduces Awakened Empire resource income and fleet power, and also increases the rebelliousness of their subjects, and has very large penalties at high levels of Decadence. What this means it that while an Awakened Empire might start very strong, and grow even stronger as they expand, that very expansion will eventually turn into decline, until they're weakened to the point where the rest of the galaxy can rebel and overthrow them - if you end up their subject, you just have to be patient, build up your forces, and wait for the right moment to take back your freedom
So if the AE will attack and conquer your rivals it will in fact weaken itself and your rival and then you can conquer them both.