M.K.
I agree with one of the responses that you should tell the Nanny about installing a camera. If she's a good Nanny, she'll think it's a great idea as it will protect her as well as your kids. I completely understand why you'd want to install one to make sure she's a safe caregiver. Again, a "safe caregiver" should see little problem with that. What if your daughter hurts herself out of no fault from the Nanny (runs into a corner, trips herself and falls, etc.), then you'll both feel good about the fact that no one was to blame.
However, I'd be very cautious about letting anyone other than you watch the tape, including your husband. Imagine if your nanny spills juice on her shirt - taking it off to rinse under the sink may not feel odd in front of two little girls, but it'd be a terrible feeling to know your husband or someone else had seen that. So you should really discuss that with her first. Perhaps even write a contract - safeguarding you both.