Princess Poops!

This weeks Special Saturday theme is toileting and our journey is still ongoing.
We started training Lucy when she was two years old, which I guess is about average in our part of the world. We tried a potty but she wouldn't sit on it, we tried a toddler toilet seat but she wouldn't use it. She hated not having a nappy on and despite trying every toilet training trick in the book we just couldn't get her to go.
We gave up and left it for six months before trying again. Again we were not successful. We tried several different types of potties, one lovely one looked just like a throne, she liked it, but wouldn't use it. We tried a Disney Princess toddler seat on the toilet with a special step. We even painted the littlest room in pretty pink so she would like it more in there. Every time we sat her down she would just scream the house down.
At three she started full time nursery. They suspended her a few weeks later and told us we could take her back when she was toilet trained. We'd tried to get away with it by using pull-ups  but as Lucy was just not using the toilet at all she was soon found out.
So we just persevered and although it was a nightmare time we finally got her to pee on the toilet. She still screamed but at least she was peeing as well. After a while she got better and would stop the screaming and just go. We rarely had any accidents and pretty soon she was dry throughout the night too. Success.
But as we all know it's not all about the pees. The poops are still an ongoing problem. Lucy suffered terribly with constipation for many years, eventually we got it under control with diet and sugar water and once they were softer she would go more often and get less constipated. But where she goes is in her pants. The past year she has got better, but she still starts to poo in her pants and then goes to the toilet. At school she just never goes, she waits until she gets home. Unfortunately just the other day was the first time she pooped herself at school and because of her age I had to go and clean her up. It was just before home time so I took her straight home afterwards and hopefully her classmates do not know what had happened as children can be so cruel.
We have talked about this problem with her psychologist who has promised to get her investigated as she may have a problem where she does not actually feel the need to go until it's actually on it's way out. It does seem that way but Lucy doesn't understand. We have tried taking her to the toilet at the same time every day, about an hour after school, which is when the accidents tend to happen but even if we make her sit on the toilet she doesn't do anything. Then she will poop her pants afterwards.
Going out is awkward but we just take a pair of pants and some wipes and just hope that we can get her to the toilet as soon as possible when it happens.  We don't know if this will problem will ever get any better, at the moment we don't have much hope.