I'm in a similar situitation. I'm only in my second year, but I know that I would very much like to do my residency out of state. My divorce is not yet final. I asked my attorney about my being able to move my daughter with me. She told me that if I were to rank my home state as #1 and not match here I shouldn't have any problem leaving. Basically it's like I tried to get a job that wouldn't require a move and didn't get it, so I've got to move to support myself and my child. My plan is to let the director here know that I'm not truly interested (if that's what I finally decide) in doing my residency here, but will be ranking them for legal reasons.
Now my attorney did say that the age of the child mattered. My daughter will not have started school yet when I'm starting residency. Apparently the older they are the more the courts frown on relocating them.