I had a student who had significant encopresis. So you need to rule that out.
I also had a son who was potty trained much much later than everyone else. In fact, he wasn't dry at night until 12. He actually had to use medication to control this. It's more common in boys, but it's definitely a factor for many girls as well. Our pediatrician sent us to a pediatric urologist, and at 7 our son went on medication (DDAVP). It was a breeze. He went off at 10, the problem came back, and he went back on until 12.
We did the alarms and felt they were pointless. They only went off after he was already wet, so what the hell was the point? It was just mental torture for everyone.
He was about 5.5 before he was reliably dry/clean during the day. I think some of it was developmental/physical, and some of it behavioral. Years later, knowing what I know about food science, I look back and wish I'd had the knowledge then to supplement appropriately to reduce the constipation. I would do that over Miralax and things like that which are less effective and don't have nutritional value.
However, beyond that, I think you're in a power struggle that you can't possibly win. I think Starr B. has some great points you should consider. There are much better products now for kids who aren't yet in control. Really, wouldn't this be better than cleaning up poop, changing and washing pee-soaked undies, and having her embarrassed and possibly made fun of in school? Cut back your expenses somewhere else, put her in appropriate garments, and let her live her life. She'll get on board faster if you take the competition out of it. No more stickers, no more prizes, no more nagging to please sit on the potty. Tell each child that it's up to them to do it when they're ready. Like walking, talking, riding a bike - it's on their schedule. We finally did the medication because we were way beyond the normal window, and he was old enough for sleepovers but couldn't' go.
Give your daughter a special bag with a fresh pull-up in it to take into the bathroom to change herself. That way, she doesn't have to take her full backpack and no one will know what she's doing. Or she can go to the nurse to use the bathroom and clean up. She and you can work out a silent signal with the teacher that says "I need to leave and go change."
Put a waterproof pad on the mattresses. We used a flat crib pad that could be washed. We put the mattress in plastic, then a fitted sheet, then the crib pad, then a 2nd fitted sheet. If our son wet through, we just stripped the top sheet and the crib pad, and were left with a dry sheet below that. So there was no middle-of-the-night bed changing. Just a pack of wipes and a plastic wastebasket for a quick wipe.
If your daughter gets a rash, try Balmex cream - we found it more effective.
Good luck!