That is a tough call! I am having a similar situation (family going on mat leave but not sure of what month yet so it is hard to fill the spot with no set date!).

I would personally do what is best for your business. It will be tough asking them to leave so maybe you can talk to them and see if you can work out a mutual date for the child's last day so it will work for both of you. Does this p/t family have a backup childcare plan?