Check out leaf spring school. It's a private school that teaches up to the 8th grade and has infant and toddler care as well. Infants nap at 10 ish and 2 ish. Not sure about toddlers.

They have three locations, with nurses and licensed teachers on staff. They are accredited with the National early childhood program association.

Depending on your location, the JCC and Sprout School have great preschools too. They are both accredited with NECPA. Not sure about nap times.