Accidents at preschool help!!

DD turned 3 at the end of July and has been potty trained since the beginning of summer. She goes to preschool 2 days a week for 6 hours each day. She was peeing herself almost everyday the first 2 weeks but has since stopped once we bribed her with a treat if she had no accidents. Now this week she pooped herself both days and didn't even say anything to the teachers. She has one week to do better or she's out of the class. I'm very upset and stressed over this. She never has accidents at home but she is able to hold her pee for 16 hours, despite our attempts at toileting. Some days she uses the potty great. As far as having a BM, she always says her tummy hurts and then she either has to go immediately or the urge passes. I don't think she quite understands the physical feelings as far as giving her much warning.

I really want her to go to preschool and not have to go to the Mother's Day out program. How can I improve this? The teachers have no suggestions. They've sat in the bathroom with her for 10mins too. I'm not too concerned with the peeing because she hasn't had that accident in 2 weeks. But as far as pooping, I'm at a loss of what to do. They expect her to be independent in the bathroom but I find it hard to believe that many new 3 year olds are.

Any suggestions?