is Ziggy mostly outside or an outside-only dog? She might be jealous of the other dogs, or feels isolated from the "pack". . I dunno, I'm just guessing.

I hope everything works out with your pups! It would be REALLY sad if you had to re-home her and break them up . . it sounds like separating them won't be too much, and I'm sure they can still play (at least, Ziggy and the dogs she gets along with) as long as its very closely supervised.