I think I am a walking expert on this now...I went through almost a year living this nightmare with my daughter.
Please believe me, she doesn't "want" to pee, she "has" to pee!
I never really found out what was "wrong" with her. They didnt want to test her for Lactose intolerance because its pretty invasive. We checked for UTIs several times and a couple times there was something and most of the time there wasn't. PLEASE make sure they coulture the sample. the quick in the office test will only show severe infections.
In the end, we took her off milk and gave her soy milk for a while. We left all other dairy in her diet, just changed the milk. She got worlds better. We then switched her to Asodopholis milk and that worked well also. She is now back on regular milk but no more than 6 oz per day. We monitor her dairy intake and make sure she isn't eating too much of it. Also we make sure she gets probiotics every day.
Little girls are very sensitive "down there". they are affected by a lot of what they eat and digest. Even a little irritation can make them feel like they have to pee when they really don't.
I really wish I had had someone tell me all this when I was going through it. I would have been so much more patient with her.
P.S. since we have gone through this, I have had countless other moms come asking for advise for their 4 year old daughter. Check mamapedia, you will see its pretty common!
Best of luck to you and Keep fighting till you find a solution!