I agree that it sounds like you have treated her very well and she has been more than compensated for her work and dedication towards your children. That said, she seems to have some problem with you and instead of hashing it out, is passive-aggressively giving little clues. I do this sometimes too, thankfully Im grown enough to know this does nothing but damage relationships. I guess it could also be burn-out, but she has had a good thing going, its hard to imagine getting burnt out with all the perks of her job, but it can happen, I guess.
Kind of reminded me of a falling-out I had with my neighbors. I became good friends with them, and our children played together, especially our 2-3 year olds. Their son was horrible to my daughter. He hit her, threw things at her, and was just awful. He cussed-screamed at everyone and that included his parents, and he would walk into my house when I wasnt even home (walking or something, I had to lock up). The whole block thought he was awful, he ran loose alot, destroyed property and screamed nonstop. The mother complained non-stop about him, and I could clearly see things they were doing to perpetuate his behavior, but I never said anything. Figured it was their kid, and they would probably get mad over me having advice/criticisms. It got worse and worse and I ended up HATING these people. They never knew how mad I was at them, as I tried to simply handle things by limiting my exposure to all of them, and that meant the kids couldnt play together or anything.
Had I spoken up about how I Felt about their child and how he destroyed my property, and was a general nuisance, maybe we coudl have come to an agreement. But I didnt. I just got more and more angry and in the end, they just thought i was a big old witch for no reason (because I never SAID anything). Your sitter seems to have some sort of problem, but isnt speaking up (except in little nit-picky ways). Maybe you shoudl ask her. At the very least, tell her you are concerned about burn-out. It would be great for everyone if she would just open up. Then you could either resolve things, or decide for sure whether or not this will work. IT would be tons better than how I handled my situation, that is for sure!!!!