Unfortunately I haven't had my homeworld taken in any of my games yet but I just loaded up a save and played some whack-a-mole with an AI's civ capital out of curiosity.
It appears to be totally random. It will even select low planet class colonies that can't become a Core World. I also allowed them to retake their homeworld and after taking the then current capital it didn't return to the homeworld. I retook it and verified it still had the Capital City building. Seems well outside the realm of player influence.
This was the "cleanest" partial solution of the testing I did earlier. There is technically one method I tried that includes all races but was much buggier as it only allowed any given planet to be named Civ Capital once. I'm not sure if I'll be pursuing this any further.
I also agree with DivineWrath and that this would require Dev attention.
