They didn't really say, as far as I can remember. They said he quit his job in NO to move to Virginia with JJ but he could have gotten another job with the police there. They just never said. I'm not sure about JJ's mother; I don't really remember that so it could be, I guess. But I don't think anyone would fault your fic if you take some liberties with JJ & Will's home life. We really don't know much about it.