M.F.
I have a friend who is a professional nanny (I believe through Mom's Best Friend) and she is $10/hr or more. If this person is truly a nanny and not just a babysitter, she should be more than able to handle a routine.
Sounds like a good routine, but I do wonder about the morning nap for a 2-yr old though. Does she actually sleep, or is this just "rest time." Most kids drop that morning nap by the time they are 18 months old.
I would address it with her when the kids aren't around to be a distraction.
However, bottom line is that if she can't or won't do what you're asking, I'd find a new nanny.