3 year old potty training

My daughter is 3 years 2.5 months old. We started potty training her at about 2 years 10 months. We wanted to wait because we were moving and have an infant. We didn’t want her to regress. We have her in training underwear. She is not in daycare. My parents watch her while I work part time. We prompt her to go every hour. We had a few weeks where she didn’t have any accidents. She has chronic constipation. We have given her prune juice since she was about 1 years old. After an episode where she didn’t have a BM for 1 week she has har accidents more frequently. We do not give her treats but she likes to get claps when she goes. She won the preschool lottery and will start in the fall. I get nervous that she won’t be trained by then. I am not sure what we could do better to help her.