I know what a nightmare it is to find day care and I can only imagine the stress and anxiety of trying to find a solution at this late date. Ugh! You have my sympathies.
I know the OP feels she made it clear that the children were (in my words/interpretation) misbehaving brats. But haven't we all been in a situation in which we agree to do something and then once we are in it, it becomes crystal clear that the situation was misrepresented, or that we are in way over our heads, or that the situation is far worse/more difficult than we imagined and we don't have the skills to handle it? As much as it sucks right now, the babysitter probably did the parents a favor because she simply could not handle those kids. Two kids who are difficult being at home without proper supervision... Well, that's a very bad thing.
I admit that even though as a parent I have total sympathy for the nightmare of finding care, I also have some sympathy for the girl because I have been in a position of watching kids (as a favor for a friend when I was an adult in my 30s) who were brats who refused to listen to me, fought constantly, and one of whom was really a holy terror. My friend had asked me because she was in desperate need and I've never had a problem getting kids to behave, so we both thought I could handle them. Until that night. Total nightmare. I still remember how relieved I was when my friend got home. I instantly told her, "NEVER again." (She was shocked that even I could not handle them, but the reality that I refused to sit for her kids again was the turning point in her deciding to really do something about their behavior.) The thought of watching kids like that full-time would be enough to make me break out in hives. And $10 an hour would not even be close to cutting it, no matter if someone else accepted that wage previously.
I will also note that my dd makes considerably more than the minimum wage (almost double minimum wage) to babysit two very well-behaved and easy-going kids who adore her (and no housekeeping), one of whom is still young enough that she often spends a good bit of the babysitting time napping.