If you contact the sanctioning body (the one that you need the player released from) they will direct you in the proper steps to be followed to have the player released. If the player in question has not played in a tournament sanctioned by that body this year, they will be more than happy to release her for you. ASA, PONY and USSSA have become very aware of the problem that you are experiencing.
Be assured that if you have a reputation (history) of jumping teams, they will make you jump through quite a few hoops to get the release you want.