Maddcow I feel for you! I just do not know how Nannies survive especially today! In my experience, my friends' DCh are taught how to bring up their children by their Nanny! Bluebell is right of course, you must keep a polite relationship with your employers, but I would still have to put in place a few "Nanny's Rules" about safety especially - you can't negotiate on that! As for TV and computers, I would try and tell them what your professional advice is, and say you insist on a certain amount of time in the fresh air and for other interests.
My first career was as a teacher, it was easier to say "That is how we do it in School" than for a Nanny working in their employers' own home.
If you cannot agree, I would tell them they would have to find another Nanny as you cannot reduce your standards.
Wishing you the best of luck!