excon is right here. The issue here has nothing to do with the type of life that can be provided by moving. The issue here has to do with the non custodial parent having court ordered visitation. ANYTHING that results in a change in that visitation has to be approved by the court. Generally if the non custodial parent won't agree, then the court won't allow a change.
If you want a change, I suggest getting a lawyer familiar with Family Court, who knows what will sway the judges.