I do what you have done. If someone wants a place to sit empty for their benefit they pay for it, full rate. I think some provider here do a 50% holding fee for a max of 3 months. I not have special template or anything. I just date contract from day they begin paying for the place. They are welcome to come all 5 days if they want to since they paying for all 5 days. It not refundable, or transferable. All my client pay for their place regardless of attendance. This no different. If mom go back to work before expected Jan start, it okay for her to do anytime after September.
If you decide to close, you would have to give notice period and this client no different.That said, they might have case for refund of holding money so maybe check with lawyer.