K.R.
There are three things you can't make a child do, eat, sleep, and eliminate. You can put food in front of them (you could even stuff it in their mouth), but you can't make them swallow/or prevent them from throwing up. You can confine them to a bed for hours on end, but you can't make them fall asleep. You can tie them to the potty, but you can't make the pee or poop come out.
I had a friend who did the three day potty training with her son, and she REFUSED to go back to diapers even when it was clear he was not on the right path to being potty trained. What she did instead was clean up accidents three or four times a day for about six months. He even pooped in the climber at Burger King!
I understand the feeling that you have to get this done for school, but a preschool that's really worth it's salt isn't going to have that policy because they will have a TRUE understanding of preschoolers. Some children are not ready until they are almost four - maybe they can hold it for three hours or more, maybe they can pull down their pants by themselves, maybe they can tell you when they need to go... But if they're too scared to sit and go, then they aren't ready. Usually the emotional piece it the last to come.
My son wouldn't go poop on the potty, I tried and tried. Telling him there were no more diapers, sitting him regularly on the potty, promising treats or toys... NOPE. Not gonna do it! He held it in for three days, and that was when I KNEW we were done pushing the issue. I'd rather have changed poopy diapers than end up in the ER with a severe blockage. He was almost four by the time he finally did it, and he did it all by himself when I was out of town and his dad was busy in the garage, then came out and announced it!
You can continue to push and bribe and insist, but she will only do it when she is ready. A child can feel your urgency on the issue, and usually uses that against you. I would take a "whatever" approach, and put it in your head that you may be putting school off for another year.