I had an awful nanny position a few years ago, aside from being watched like a hawk, and given a huge list of dos and donts, I was publically ridiculed if I made a mistake. I was 24yrs old at the time! I had around 6yrs experience, and a child development degree, but I was shy.
It was an extreme family, and one like no other, but my biggest regret is leaving without having a discussion with parents first. Not only could I have defended myself, and said what I wanted, it would have given the parents the opportunity to see that I do know what I am doing, and I am worthy to look after their children.
I have dealt with enough parents over the years to know that some just can't let go, and need that control. (Some, in my case, excessively so) but we have to realise, that these aren't our children, they are someone else's most treasured "possession" and actually they have every right to a few batty demands, providing there is a mutual respect.
Whatever decided, to stay or go, I would definitely say you need to talk to them. You both may agree to make changes, or you both may agree to go your separate ways...I think you will regret it if you don't let them know how you feel!