And you need to use spelling and grammar check.
Sorry it didn't work out.
She told you she wouldn't be back. You need to fill the spot. I hope you sent all of her stuff home with her and charged the full notice fee.
In the mean time, figure out what to do differently with a new client. And never, never ignore a parent's question. If you have already answered it, begin with "If you will remember from our interview, ..."
You need a late fee and a full day fee. Don't bother doing it by the half hour.
And no, being your mother is not an acceptable credential for surprise caregiver. Diapers SHOULD be changed every two hours. One runny poop is a call to pick up. Once you have allowed flexible pick-up you either correct and adjust contract and fee or deal with it. You CAN see a teether without putting your hands in a mouth, and that seldom causes diapers to leak. You should know if they fit or not. Two hours is too long to be outside all at once in this heat (in most of the country). I could go on.... But since I care about you and I know that you are probably feeling bad, I will just refer you to the Purdue writing center for tips on business letters, and mention that I can tell you are both genuine and intelligent from your writing, but that you need a little practice and you deserve to know that the word is 'hence'.
http://owl.english.purdue.edu/owl/resource/653/01/