I was reading this and thought I read it before so I'm guessing it was one of the vanishing posts of the week. LOL.
I would not state an end date on the contract. WHY? What if the boy who is suppose to replace her full time summer spot come fall falls through? Also, if you have an end date of the contract then a week prior they don't pay stating they gave you a week deposit and they claim to attend part time, but don't show up the day after the contract expires to start part time....then you're out of two weeks of pay AGAIN.
I would keep the email simple and short. You don't need to lure this family into taking your spot because they're already wanting it. I would email and say
I have a temporary full time spot available for CHILD'S NAME for this summer only. A part time position may still (say may so it's tentative) be available in the fall. Please give me a call (insert phone number) so we can arrange a time to meet and sign the new contract and discuss the details. Talk to you soon, YOUR NAME
Then when she calls you can discuss the hours she needs care just like you would anyone else. Then let her know the full time rate and that a one week deposit will be required the day she signs the contract. Invite her over to sign the contract and go over any questions she may have. Have this just be a normal contract and just keep communication open for when the position switches to part time. You may even require in your handbook or contract that a change in enrollment status requires a two week notice and approval. If you just want to keep the lines of communication open, just remember to discuss the hours and ask her two weeks or so before going part time to sign a new contract and have you spend ten minutes or so with you. I just don't like the idea of contracts going home with people, they should be signed infront of you so you make sure they don't tamper with it at all.