It's "normal" for a school to have a policy for potty trained kids. If they only accept potty trained children, then a child that is not potty trained would take away from the rest of the class. A school must decide what they consider "potty trained" and evidently 3 accidents in a certain period of time means they are not potty trained. I understand their rule about the 2-week suspension and the no pull-ups rule. Either a child is potty trained or not. Children have accidents (of course) but pooping 3 days in a row is more than an accident.
I also understand them not cleaning your daughter up, in a lot of situations they aren't required to clean up a child if they've soiled themselves. That doesn't mean a person can't have compassion and try to help out, but they are not required to. When a child vomits or soils themselves, as a day care worker I am not required to clean them up. However, that doesn't mean I never did.
There is NO EXCUSE for the school to be rude or embarass you or your daughter in any kind of way. It's traumatic to poop your pants! No wonder your daughter did it more than one time! She's probably embarrassed.
Observing one day may be disruptive to the school--and if they let you observe, then they have to let everyone observe.
If I were you, I'd just talk with your daughter and her teacher to find out why this is happening. This doesn't sound like a potty training issue at all, it sounds like a school issue. Is your daughter nervous at school? Sometimes kids feel the need to poop when they get nervous. It's a normal reaction. She may also not feel comfortable asking to go to the bathroom since she probably has to raise her hand and ask in front of EVERYONE. That in itself can be embarrassing! Find out what the bathroom rules are. Some kids feel nervous around the teacher and her authority, some don't understand the rules, and some are uncomfortable. You just need to find out what the issue is, and also what their bathroom policy is.
Some kids also aren't comfortable pooping in a "public" or strange restroom. I know I'm not and I'm an adult! If your daughter is feeling like she has to go out of nervousness, but then can't bring herself to go in a public place, then it may come out later when she can't control it. She's only 3, still very much a baby.
She may also feel rushed in the bathroom. Pooping takes time, no one likes to be rushed. She may also want to get out of the bathroom to go play, something my daughter used to do. She'd hold it because she was so excited to be playing, and then it would come out later.
Some teachers also may not fully understand. They are busy, and if your daughter just went to the bathroom, if she asks to go again the teacher may say "but you just went!" Your daughter may have to poop the second time, but is being turned down.
You just need to find out the "why." There are lots of possible "whys' and I agree that sending her home to be "retrained" won't help. It's not training, it's something else that needs to be addressed.
I think that 3 year old are still babies, and people need to be more understanding. We are so into our kids growing up so fast that we forget they are so young.
Good luck! I hope you can figure it out and your daughter can stay since she loves the school and the kids. If the school won't help you figure it out, then I'd find a different school.