First off, as a nanny I take outside gigs for one of two reasons: either the family is filling a need for me (e.g., babysitting for a newborn helps me be content with my preschool-aged charges the rest of the time, or taking elementary schoolers to the park on a Saturday helps me be content with the boredom of being in the house all day with an infant charge). The other reason is if I need the money. If you are so concerned about the quality of care droppin because nanny is overworked, let me tell you that a nanny who is stressed over bills burns out much faster than one who does occasional date-night sitting.
But the bigger issue here is: you get to tell the nanny what to do for every hour of her time you have reserved and paid for. You have zero input into any other time.