Disconnecting life support is one thing. Forcing the girl to stay in that hospital violates the parents' rights. Wasn't that actually what the issue came down to in the Terry Schiavo outrage?
They're not trying to take the girl home. They want her admitted to a long-term care facility. Until now they haven't been able to find one. They are also being asked to by hospital to provide, in writing, a plan for the continued care of Jehi. They have not done so. Perhaps now they can. Also at issue is the insertion of a feeding tube. Doctors at her current hospital will not perform surgery on a dead person, as Jehi has been legally declared.
In Schiavo's case, her husband was her primary next of kin and legally allowed to make medical decisions on her behalf. He made the argument that Terri would not have wanted to continue living in her condition and that prolonged life support should end. He was challenged by her family in a very acrimonious and public battle but he ultimately prevailed in the courts.