Well, it will be tricky, but I think I should be able to take it out. It will take lots of Spirecraft implosion artillery, Spirecraft rams, and a gigantic number of bombers (backed with the rest of my fleet, of course), and I would have to lure it off the AI homeworld (those Core guard posts HURT), but I think I can pull it off.
No matter what though, I am going to suffer MASSIVE losses.
Before I try this though, is my understanding correct that the AI Mothership will only spawn once per homeworld? That is, if I do somehow manage to kill it, will the AI just spawn another one once I go onto the same homeworld again?