I don't understand. If the mother is willing to pay for continued life support, though futile, why won't the hospital agree?
Because further care would be futile. Hospitals are under no obligation to continue palliative care when there is no hope for recovery.
In Catholic theology, this child, on a ventilator, is receiving extraordinary means of life support, and there is no moral obligation to extend extraordinary means of care.
If the child could breathe on his own, but with a feeding tube, the hospital would be in a different situation, though it would still likely ask the mother to find a long-term care facility for him.
I hate to see cases like this, but this situation has one enormous difference from the Schiavo case in that Schiavo was capable of breathing on her own, where this child apparently is not.
Hospital resources?
Where does it say the mother is paying? Either the hospital and doctors are paying, by providing services without payment (and charging other patients more to compensate), or the taxpayers are paying (at Medicaid rates, which don't cover costs, and again force the hospital to charge more to self-pay and insured patients), or an insurance company is paying.
And let's be clear about what sort of order this court issued. It's not a "restraining order", which would prohibit someone from doing a particular thing. It's an involuntary servitude order, in which unwilling hospital staff have been ordered by the government to continue providing a service which they do not wish to provide, do not believe is ethical to provide, and are most likely receiving little or no payment for.