My roommate is divorcing and moving to another state.

I can't imagine him being able to get custody or prevent the move, what with his history of domestic violence, failure to pay reasonable support, as well as his criminal record.  She may have to request permission from the Court to move with some litigation over it.  She could take steps to force him to pay reasonable support which may put additional pressure on him to cease interferring with her life.

Under these circumstances, it would not be likely that he could oppose her relocation.  He has to establish a history and desire of being an active father and a supporting father.  It appears he won't be able to do that.  If she is looking to leave the state and wants to stop him from being able to block the move, then a petition should be filed with the local Family Court and she would be well advised to consult with an attorney on the issue.