Odd, the exo-waves aren't supposed to stop when the minor-faction Spire spawn, it's supposed to keep coming fast and furious. In my tests, I had to keep defending myself despite the assistance (though it wasn't as knife-edge a situation). I saw the same situation in some of the beta-tester games too. So it sounds like there's a bug in there; do you have a save, preferably before completion of the last structure?
As for the Motherships, remember that they were added much more recently for the purpose of making it harder to win with your own spire fleet. Since Motherships contain a core-shield-generator (making it impossible for anyone, even the minor-faction spire, to even damage an AI Core Guard Post or AI Home Command Station), they are instantly destroyed by the subspace pulse that the minor-faction spire generate to take down the core-shield-network in the first place. One thing I could do there is have it spawn a variant mothership that doesn't have the core shield generator. Depending on placement when spawned, a mothership could actually destroy an entire SD-led fleet, but it's doubtful that it could really make you lose, so that would be ok.
Anyway, thanks for the feedback, sorry about that bug