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Does he ensure that he has these weekly visits?Why are the supervised?
Why are the visits for only one hour a week?
It is very difficult in most cases to convince a court to allow a parent to move a child away from another parent. The reason why is that the court must makes its decision solely based on what it determines to be in the best interests of the child. And generally, it is considered best for children to live in close proximity to both parents so that both parents can be involve in the children's lives in meaningful ways.
Your fact situation sounds like you have a stronger case than most parents do, because it seems like you have a father who does not have much interest in being involved in the child's life. For this reason you may very well be able to succeed in getting a court order allowing you to move your child. Your next step should be to retain a family lawyer who has a great deal of experience in mobility rights cases. In fact, you should try to retain the most experienced lawyer you can afford.