Hi. I'm sorry for this happening to you. No one better than us know how hard is to loose a client that signed and backs off. But, also I have noticed some people fails to think or view things from our side because they aren't aware of how this business work. If you have opportunity explain to them on how detrimental is their cancellation to you, explain how much work it takes to interview families and find the right fit and then to contact others to tell them to move on because you're full.
Explain to them that at the end their two weeks notice might not even cover all the finantial loss of one empty spot; it might take you more time to fill that spot and sometimes months, which a two weeks deposit doesn't justify.
You can give their receipt but not the extra.day payed, two weeks is ten payable days to us. Even if they're starting a day after a holiday, I would personally count as ten days deposit. That is covered in your contract. If a child starts let's say in the middle of a week I just ask to them an extra check for the days that he was is care and I charge the two weeks later on.
So review your contract. When we say two weeks holding deposit it is 10 days in my view.
Good luck, hopefully someone fills your spot in no time. And even if you do and if they notice two weeks of pay for the inconvenience sounds fair.