OP, what exactly are your childcare expectations for your nanny? You've been pretty clear on household expectations. And posters have mentioned that depending on the type of care, household expectations might be different. If you're TV-free & having the nanny rock your DDs to sleep, that's a different thing from having them watch some TV or highchair play-time.
We have a nanny share, so a sort-of-similar set-up (two children almost the same age, currently toddlers) & to me, this list sounds like a lot. We have rules about no-TV/screen & making the kids the priority & I know that our nanny is on the ground with the kids most of the time, so I kind of want her to take a break while they nap (and nap time is totally variable between the two kids, so even if my son takes a 3 hour nap, the way they overlap it may end up that the nanny only has 30 minutes to herself). She does what she can do, and sometimes it's totally maddening to discover unexpected messes. But it'd be way more maddening if the kids didn't love her as much as they do.
By the same token, I can totally sympathize with many of your experiences -- It really is difficult to have someone who is basically a stranger all the sudden an intimate part of your life & (as someone who's also adverse to confrontation) it can be really difficult to be the boss.
So, ultimately, my advice is to pick the things that are really important to you & discuss them with her. Figure out what stuff really is minor & just determine to let them go. If you're not going to bring them up with her, you really have to just let go or it'll drive you crazy & possibly drive a wedge into a good relationship.