I like what Peg and Lynn have both suggested.
As someone who has worked with kids for a long time, and in a variety of settings, I have a certain degree of empathy with you. I do understand how chronic diaper rash can begin to seem 'neglectful'. At one daycare I worked at, we had a toddler who would come in with a bloody red bottom on Monday. My team had one goal for this little girl: getting her bottom cleared up. Diaper changes were huge screaming tantrums on Monday and Tuesday because they hurt her so much ( and we did everything from more frequent changes-- once every 1.5-2 hours-- to rinsing out wipes, etc.). By Wednesday the rash wasn't a screaming terror and by Friday her bottom was healed again. But come Monday-- all our hard work was gone, and her bottom was bloody red again. And we'd tried every method of parent communication/education we could think of, but nothing seemed to sink in. So, yes, in my opinion, this can be considered neglectful.
I don't have much more to add than two other points, and I'll try to keep them brief: first, if you are done with this woman, it's okay to be done. I've worked with some wonderful parents in my time, but there were also those who seemed a bit rude/nuts, and it never really did 'get better' to work with. In fact, those working relationships tended to become more and more fraught with problems, just because some parents are working from a very different perspective and don't see their responsibility within situations of their own making. You *can* try sitting down with this mother, but only if you genuinely want to improve the relationship and the health of the child. Be prepared that this conversation has the potential to end badly, because she isn't asking you for advice and will perceive this as direct criticism of her parenting. (I've learned the hard way not to offer advice unless someone asks.) And she may not "hear" you at all, but only what gets through her filters, so once again, you will have to be the one grounded in reality going into it.
The other thing to keep in mind is that you are doing absolutely the right thing to keep this child separate from your own. Even if this woman only sees the inconvenience--- and not the harm-- of bringing her child into your home, it's simply not good form to be getting upset at the care provider for this sort of exclusion . Assumably, she'd want the same regs in place if her child were the healthy one.
I know you have some choices to make here. If it were me, personally, if you choose to continue care, I'd create an exclusion policy and go over it with her, and have both of you sign it. (Explain, too, that if YOUR child is unwell, that these rules apply and that you will have to cancel care.) People often forget that having a care provider doesn't excuse them from also finding backup care, which is a necessity in any case.
Or, you could always make your life simpler and tell her that you are finding that this care arrangement just isn't working for your family and that you will be done on "X" date, and give her as much notice as you feel is reasonable. Then, if she wants to quit early, that's understandable. Sometimes, some parents are just more work than their kids are, and it's okay to say "I don't need this kind of drama in my life". My guess, from your description, is that she's a parent who may need a lot of parenting/health education, and may or may not be receptive to it. It's okay to say "I don't want to continue to support a parent who is showing no reciprocity, or even a willingness to have these conversations." It's up to you...
H.
(Oh, and in answer to your last question-- if it were me, I'd ask her to make other arrangements. But I'm 40 and tired and as I sometimes like to joke "just too old for this sh*t!" I don't choose to deal with unpleasant people on a daily basis, thanks!)