I second the response that 3 is not late.
We had to have my daughter trained by the time she started preschool at a private school in Dallas. She turned three in late July and school started in late August (this was three years ago). I was stressed trying to make it work, and felt like we were pushing her to meet the school's requirements instead of letting it happen on her timetable. Most of the kids in the preschool were 6-12 months older. She ended up being potty trained and it wasn't as big of a struggle as I thought it might be.
We put a sticker chart on the mirror next to the toilet and each time she went, she got 1 sticker, but if she pooped, she got two stickers. She got to pick out the sticker(s) and place them on the "chart" which wasn't a very structured chart - just a white piece of paper. She loved getting to place the sticker(s) wherever she wanted. Once she got X number of stickers, she got to select a prize from the prize bag. The prizes were cheap things like a box of crayons, a toy ring, etc. We only used the chart and the prize bag for a month or two max.
Does the school have auto-flushing toilets or was she exposed to one? I have heard several stories of children being afraid to use any toilet after their experience with an auto-flushing toilet that goes off before the child is done. I saw the recommendation to put a sticky note over the flush detector so it won't go off.
Good luck!