Is there anyway to compromise...like pay for the cheapest dive motel room for three days...help him get to his appointment on Monday. One, it gets him out of your house...it might make the transition to a homeless shelter easier, as he would already have a backpack with his essentials.
You could notify his psychiatrist today what is happening...so maybe he would have a plan B. Difficult Child might be more motivated after staying in a hotel room with a loaf of bread and a jar of peanut butter... KSM