OP - MB here. I set the schedule for the most part. I can see what is and isn't working based on how the weekends are going and I also factor in our family's needs (i.e.: can't have younger DC napping when older DC needs to be picked up from school, go to an activity, etc.). However, nanny and I typically discuss any changes and she voices her concerns or opinions. She recognizes though that although she is with the kids for 40 hours a week, I see the whole picture. For example, DC was falling asleep during his "quiet time" regularly and clearly still needed a nap, but it was seriously impacting his ability to fall asleep at night. He was waking up for school in the AMs cranky and tired and acting out badly at school, and then falling asleep every afternoon. I know it was easier for nanny to have older DC "resting" when younger DC was napping and clearly it might look like he needed the nap, but in actuality, what he needed was a good night's sleep. I asked her to keep him active during his "rest" so we could put him to bed earlier and although it was painful for the first two weeks, now everything is better - his night sleep, his behavior at school, and the need for a rest in the afternoons is gone.
That said, if the schedule gets thrown off by 15 minutes here or there - or if the kids look like they need to eat early or nap late or if it's a special occasion or whatever, that is just life? Happens with us on the weekends too. But a lot of that is built on mutual trust - I trust our nanny to adhere to the things that are important to me when possible, and I trust her to make the right decision when our set schedule doesn't make sense.