J.O.
I have had the same issue w/ my almost 4 year old daughter, she was potty trained at around 2 but come the 3's she started to do the potty dance, and like your daughter she would say no she didn't have to go, know for me it was extremely important that she didn't hold, she was born with only one kidney and this could lead to infections if she held it, at first it was no big deal but then it became a habit, I tried having her clean it up, no big deal for her, she just cleaned it up, most of the time she made it to the bathroom just not onto the toilet. I was staring to get worried about the amount of times she was holding it, I finally sat down with her one day while she was on the potty and just explained, as well as I could to a 3 year old, just how bad it is for girls to hold back there potty and not go when thier bodies are warning them that they need to go, she knows she only has one kidney but becuase she is healthy it doesn't really have an impact with her, so I explained that when we hold back the pee it sits in our bodies and that our pee and poop is a way for our bodies to get rid of all the bad stuff and that if we hold it the bad stuff stays in our bodies and can make us sick. I did have to repeat this over a few days but I think it did set in her brain because the only tiome we have an accident is when she just can't get to the bathroom on time, and once in a blue moon at night, maybe this will work with your daughter, I had to get creative becuase it was nesaccary, hope I helped even a little.