I would base it sort of on how long you have had the deposit as in how long have you not been interviewing because that will effect how long it takes to fill the space. If she can find someone to start before Sept then she will get her money back and if not then well that is the point of the deposit.

You could agree to advertise and interview and only if you find a replacement the refund will be returned as in the deposit placed by the new family becomes their's.

I changed my deposit to apply to the last two weeks of care. IF the parent starts care in sept then she pays accordingly and then is allowed to give notice. Until care actually starts the contract doesn't go into effect. Meaning she can start in Sept and pay for her first week of care and on the same day give notice to terminate and pay anything beyond the two weeks of care. The fact she told you early is a bonus and effects nothing. The money is yours if she doesn't start care in Sept. If she starts care in Sept then the rules of the contract start too - ie length of notice.