Our daughter was exactly like that, woke a lot at night, short sleeps during the day. We eventually worked out she just didn't need that much sleep. We also would bring her to bed with us at about midnight and if she stirred one of us would just rub her back or tummy till she slept again. It was the best thing we could have done. In stead of fighting to get her to sleep more, we just adjusted our lives.

Now she is 5.5 and goes to sleep at 7.30 ish and gets up at 6ish and entertains herself with animals and toys til we get up at 7. She still does wake occasionally and we just co-sleep or put her back in her bed, depending on how we feel. (sometimes we just want cuddles!)

HTH