According to TX State Minimum standards, if a child isn't napping a teacher is required to give them an alternative activity, (I'm not sure exactly how it's worded, but I know it's in there). Books, puzzles, playdoh, coloring, etc. are all good quiet activities. The teacher and director have unrealistic expectations if they expect a 3 year old to lay still and quiet for 2 hours!!! I would talk to the director about this since you've already talked to the teacher. Especially since this wasn't a problem in his last classroom.
(I worked in daycare for many years before staying at home with my kids. We always gave the kids a quiet ativity if they didn't take a nap.)
EDIT: I looked up the Minimum Standards for you. Here's what it says:
"Naptimes, or a period of rest for those children too old to nap, during which children should be supervised according to §###-###-#### of this title (relating to “What does Licensing mean by “supervise children at all times”?)....
...Naps and rest time for school age children will vary with each child’s individual needs. Children in full-day care benefit from resting or napping during their long day. A rest period may be reading books, listening to soft music or books on tape.
See §§###-###-####-###-###-#### for additional minimum standards on naptime."
http://www.dfps.state.tx.us/CHILD_CARE/Child_Care_Standar...
From this website, you can click on the state minimum standards for childcare centers, which is where I found the above statement. Hope that helps!