Need advice on getting 3 yr old to sleep

I have a three year old daughter who will not sleep. We have a nap routine and a bed time routine. (Story, Song) Then she will give me a song and story(she loves to do that.). Then when I leave the room she starts to get out of her bed and will run around the room. So I just walk in and put her back in bed. Sometimes she just sits on her bed, and sings and talks to herself the full nap time(which is mainly what happins.) By the time nap time is over, she is grumpy, hyper and easily frustrated. Nap time is over at 2:00. She then stays up until 9pm.We have the same problem for bedtime as well as we do for the nap. She always says shes hungry, or wants to look for a book or finds any excuse she can. Even though we have lunch before she naps. She knows when nap time comes because of our routine. She did have stuffed animals in her room, (I know that is part of the problem, so we took them out.) But other than that she has just her bed, dresser, etc.
Can anyone offer any advice or suggestions to help me? I know she needs(?) to nap, and she needs to sleep at night. But By the time she does fall asleep at night it is between 11 30 and 12 midnight. I have to stay up until 2-3 am because I cant get my stuff done because she wont nap. I have animals to care for (4 dogs and 1 cat), as well as a husband who would love more attention.