We were having somewhat of the same problem with DD when she was around that age. Actually she was ok with peeing in the toilet, and wet her paints only a little bit, but pooping in the toilet made her very upset. We could tell when a poo was coming down the pipes, so we would pick her up and take her to the bathroom and she would scream at us for a diaper. We did everything we could to encrouage her to go; treats, sitckers, glowsticks, lots and lots of praise, special songs, special jewelry,special phone calls and it all did nothing. We even told her that if she went poo poo in the toilet 10 times, she would a special Rapunzel tea set. Nope, still nothing.
One day we decided we would take her to the Dollar Store and let her pick out 10-12 things and explained that they would be her poo poo presents and put them on the bathroom counter for her to see. Everytime she went poo poo on the toilet she would get a present. The change was almost instant. She went from screaming everytime she was on the toilet, to trying to push one out a few times a day. We were really surprised. The first few days we gave her a gift everytime, but eventually we dwindled it down to once or twice a day to nothing for a while now.
She turned 4 in November and she only wears diapers at night, but we are so relieved at how much better she is doing now.
I understand some people won't agree with our methods, but we were desperate. We have another baby and I was so tired of changing that many stinky diapers a day.