I would go ahead and interview family B and get a feel for them. If they aren't the right fit then issue solved.

If they are a good fit and interested then since it is your business and family A has taken over a week - more than a few days to get back to you then you have every right to accept family B and then to notify family A that the space is no longer available.

One of the reasons Family A might not have gotten back is mom is still sorting out her new schedule with work. However she should have done that before looking for care so she knew what she needed.

If family A is starting right away you could forego any deposit but this would be a good place to take a two week deposit for the last two weeks of care.

For family B they should be paying a two week deposit and as playandlearn said some apply it to the first two weeks of care, some the last two weeks of care or some to the first week of the second and third month of care - ie after any initial transition either can leave without notice period has passed if you have that clause.