Dilemma

So here's the dilemma. Three out of every 7 days, Avery does not sleep during her nap. She lays in her bed, in the dark, under the covers, with no toys or books, but she does not fall asleep. Its almost as if her mind is going to fast for her to relax and fall asleep. If you stand by the door and watch really close, you'll see her lips moving and an occasional finger twitching as she tells millions of stories in her head.

So instinct would tell you that she must not need to take naps every day right? Wrong. Because on the days she doesn't sleep, she cries all afternoon long and into the next day. She's overtired by bedtime and can't go to sleep. She throws fits every time I tell her no. She has a hard time sharing and tends to get a little bit of an attitude towards the rest of the family. These are all not normal characteristics of her on the days she sleeps.

So here's the question...has anyone else ever dealt with this and have a great solution other than allowing her to skip naps? Or do I just have to deal with it and chalk it up to another one of those not so fun mothering moments? Just curious =)