@thelentil, I think you've had an unnecessary shitty time on here, but hey that's what step parents normally get!
I feel for you I really do, our change happened as dsd & dss started to get a little older, your dsc are getting to an age where they can start to make a difference.
Do the kids know they have nits? I'm sure they know about the verrucas, is it possible to buy some verruca plasters and entrust them to the child to put on? Building a reward system over them doing the basic that are needed. I know this should be done by their mum but from looking at the situation there's no chance this will happen.
I think it'll help if you look at what you can change, we know it's not her, she may even refuse to do these things because it's come from you or your dh. You can reward the kids for trying to help themselves, as someone suggested combing each other's hair, maybe putting plasters on each other's feet. I would think that a freeze application when with you and some verruca plasters in the meantime should help.
Being a step parent is sooooo tough, your reward will be when the kids are older and they will know what you did for them, kids aren't daft, it's probably going to be a rough ride until that point though I'm afraid. That's why I'd urge you to focus on what you can change, you'll end up enormously stressed and feeling so resentful if you continue to worry about the things their mother won't do for them.
It sounds to me like you're a fantastic step parent, the children are very lucky to have you, just don't let the anger eat you up. It's an easy place to get to and not so easy to get away from.
Reward the kids for using nit shampoo and combing each other's hair, also for sticking plasters on each other's feet. They're only young so don't expect miracles but I think with some persistence and positive reinforcement you'll get there.
I would just like to say again - you seem like a very concerned, conscious & caring step parent. Keep your chin up it will one day become easier