I would not stop napping a three year old child as its developmentally appropriate for them to do so-- legitimate sleep experts will back my claim up. A quiet period of rest is a mandatory part of my program. I do not force any child to sleep but I do expect all children to rest in the afternoon. Could you perhaps encourage this child to rest instead? She may fall alseep during this time. If she does its because she needs it. Three year old children should be napping at least an hour or more and sleeping around 11 hours at night. Perhaps the issue is not the nap but maybe the child is "ruling the roost" at bedtime and the parents need to take back their roles as the ones in charge. I'd encourage the parents (and everyone for that matter) to read Dr. Marc Weissbluth he is an awesome sleep expert!