Hi, have skim read the thread. Couple of things - reece, pre-schools are not allowed to stiplate that a child must be toilet trained now, as it is perfectly normal for a child to not be out of nappies at 3/3.5. They can say that they would PREFER the child to be toilet trained, but it cannot be a requirement legally!
If it helps, my ds1 took AGES to train - we tried at 2.6, and he was SO not ready and I was getting SO stressed by it all (and he was too) that we went back to nappies. Then at age 2.10 when I was getting jumpy about him being the only one of his peers in nappies we went for it. He was able to wee on demand in the potty, so I made him go every half hour and gradually increased the time between, which meant very many fewer accidents than when we'd tried before. However, it took a week away when he was 3 with some of his friends before he really got the idea.
Part of that was learning to wee standing up - as your children are a bit older, you could try that - ds1 LOVED being able to wee standing, like Daddy and his friends, and liked being able to water the flowers in the garden. We still had lots of accidents, but they were much less frequent, and he was more able to tell is when he needed to go. He's 5 now, and hasn't had an accident in ages. But pooing did take a lot longer to get right - months actually. We started asking him to try and do a poo in the toilet before bed, and after a bit (and lots of sticker charts/engines!)he got that sorted. He still does a poo every night before bed!
Dd is 2.11, and we trained her about a month ago. She got the weeing absolutely no problem - only about 2 accidents ever, so no question about her being ready. But again, pooing is difficult - we have had NO poos on toilet/potty - all in pull up in morning before getting dressed, or in pants. She always says 'next time she will do it in the toilet'. I think it just takes longer to get right.
The main thing is not to get stressed - at dd's playgroup they said they ALWAYS have a 4/4.5 year old in nappies, and as long as they're trained by the time they start reception, that's all you need. Some children just take longer than others. Good luck (and wish me luck with the dreaded poo!!!).