I don't really see the problem that some seem to be having with Kitty being the reincarnation of Josette. Reincarnation doesn't meant that a duplicate of the same person is made. Like Magnus said, reincarnation knows no bounds. So, I could be reincarnated as a poor, black, asian, arab, or otherwise non-white person who has no friends and does drugs. That would be a COMPLETLY TURN AROUND from what I am now, and my soul would still be the same.
Reincarnation, to me, means that a soul is created by God, or whomever you wish to believe is upstairs, and sent to earth to live a life. The body they inhabit dies, and they return to heaven (or whatever you percieve to be up there) and then after a while the spirit or soul, whichever you wish to call it, returns to another Earth-bound body and lives out another, completely separate and probably completely different life. The soul, during the transfer, doesn't retain the memories of it's previous lives consciously. The memories are there, make no mistake, but it's not stored in the same place where you store a memory of what you had for breakfast yesterday morning.
So, it's completely logical to me that Josette's soul could re-enter this world in Kitty's body, and she would have no memory whatsoever of who she was before, or that she even lived before, and be leading a completely separate life that just-so-happened to crossover one point, Collinwood, same as the life before.