I agree with the majority of responses. If you didn't send it already, don't. Vent to us - we are much more sympathetic.
I'm gathering from one of your last paragraphs that the parent already told you she's not coming back. So.. as per your contract, send her the bill for the 2 weeks that she hasn't paid you and be done with her. (I hope your contract says they must give 2 weeks notice.) That would be the only correspondence I would have with her at this point.
Thanks to her you will probably be dealing with sick children (and possibly yourself being sick) as I've never seen teething produce loose bowels to the point of running down the leg. If you all were going in the pool it's possibly that the child was injesting pool water and I've seen that cause havic on the guts. I hope that's all it was.
Take a deep breath and think about how much less stress you will have in your life now that they are gone. Good riddance!