Are you kidding? Parents are complaining because your preschool has a naptime? If my preschooler does not get a mid-day nap, he would be a total nightmare for the rest of the day. He would also need to go straight to bed as soon as we got home (around 5:00 PM) and completely miss dinner and spending any time with the family. I find it very hard to believe that a true parent is having an issue with your preschool having a naptime. Plus, naptime is developmentally appropriate for this age.
As for playtime, play is a child's work. They learn so much from what seems like playing. The idea is to have some time when the teacher is guiding the play and some time when the children are directing their own play. When I was a preschool teacher, the idea was to teach thematically. For example, we would spend a couple of weeks on "community helpers." This included jobs like doctors, dentists, mailmen, farmers, grocery store jobs, policemen, firemen, etc. Along with reading books about these job, singing songs about these jobs, etc., the students are encouraged to act out or pretend scenarios involvling these jobs. The teacher can encourage the play by providing items to facilitate the play - dress up clothing, props, new vocabulary words, etc. I just loved to play pretend with my students and my own children.
Now if all you're doing is allowing the children to have free-play all day, then yes, as a parent, I would complain. A good preschool program has a variety of activities. I don't know where you live, but if it's in the USA, there are probably laws that dictate how preschools should be run, including providing children with a naptime and what kinds of activities the program should include. Are the parents asking you to break the law?