Can I use my surname for school etc?
I wouldn't do that.
I understand that he has been a twat. He's probably made you and maybe his children miserable but their surname isn't his; it's theirs too. By trying to use a different name at school you would be giving them complications to deal with in the future that they could well do without and for no real benefit.
If you were successful, what would happen when they are older if your ExH puts pressure on them to start using their real name? Do you want them feeling torn between hurting you and hurting him?
Also, if you try using a different name and your ExH manages to intervene and prevent it, you're going to feel even worse.
There are things that need to happen when a relationship breakdown involves children and they are generally things that are of clear benefit to the children. This isn't. It's for you, not them.
I feel for you and I understand exactly where you're coming from but you just need to let this go. Their name is theirs, not his. Try to find a way to accept that it isn't going to change and concentrate on the things that are really important.
Don't forget that you get to be their main carer. That is worth a myriad surnames.