Giving up custody is up to you. But you will pay for child support to the fullest and lose decisioning power over their future.
I don't know how each state views custody but I know that 50 / 50 is ideal in our legal jurisdiction. If parents can negotiate and agree to where to live, courts will not deny shared custody.
You have a right to say what schools and area to live in as well. Screw her, don't fall on your sword like that. Get involved and start researching schools and areas. Bring that information to mediation and it will be extremely effective.
