Here's what "I" see the problem to be. Nap time is around noon. Stop doing this to her. She needs to eat lunch and go lay down. Train her to nap around noon for an hour or so then she will be ready for bed time.
Letting her take her nap at 4pm is....I just don't have words. Okay? Thats' early bed time and not a nap.
It's up to you to arranger her schedule. She is 3 not 1. She doesn't need a 2 hour nap plus 11 hours of sleep at night. That is 13 HOURS of sleep per day. She isn't supposed to have that many hours of sleep per day.
If she's taking a 2 hour nap during the day then she should be able to sleep at night maybe 8 or 9 hours. That's 11 hours per day for her. That's more than enough.
I suggest that you need to put in her bedtime to a reasonable hour. For instance. If she is sleeping during the day for 2 hours and wakes up at 2pm then she should be good to go until at least 8pm. Then bath and bed. She should get to sleep around 8:30 or 9 then.
If she's up by 7am she has had a full night's sleep. She doesn't need more.
So many people put their kids down so early and don't have much of a life.
I knew a young mom that thought she was supposed to put her kids in bed at 7pm. It's still daylight outside at 7pm and people are upset because their kids are wound up and wanting to go outside to play. All the neighborhood kids are running and playing and having fun outside and these parents are mad at them because it's keeping all their kids awake. Come to find out they wanted them to go to bed so they could watch the TV shows they liked but didn't want the kids to see. As the kids got a little older the oldest girl wanted to play T-Ball but the games didn't even start until 6:30 and 7:30 so the family told her she couldn't play. How very sad.
Just because someone told this mom that their kids should be in bed by 7pm. Crazy in my opinion.
You could go to parentcenter.com and search for hours of sleep a 3 year old needs. Remember though that includes sleep during the daytime hours too. If it says 10 hours then she should be able to take a 2 hour nap during the day, around NOON, and then go down and sleep 8 during the night.
I'd sit down and seriously look at her schedule to see what's going on because it just comes across that you're trying to get her to sleep too many hours during the night.