What is this help that you need so badly around the house and how often is it happening?
I can count maybe twice when I was single and living alone that I had to ask someone like my dad to come over and help with something and it was for things like my boiler playing up, car breaking down. Even then though, I was young and would expect to deal with those things myself now.
However it sounds like he's coming often to help you with bits around the house and that is excessive. What do you need help with so often? You're a grown woman, you shouldn't need your ex round all the time to help you with things around the house and if you do, I can count on one hand the amount of 'big' jobs someone could possibly need help with about the house.
However the other stuff is completely crazy. The days out, holidays, girlfriend travelling alone whilst you play happy families in another car. It's weird, it's you controlling the situation, not the girlfriend. You're not one happy family anymore OP you need to realise that. He should be doing days out and holidays with his partner. He should be travelling with her to events etc...
Yes you're the mother of his children, I'm sorry but that does not give you some sort of superiority and control over his life forever more. He should respect you (but that doesn't mean giving in to every ridiculous demand you have), and facilitate your relationship with the children just as you should in return as co parents. He should not have to act like your partner for the rest of his life. Neither of you will have any sort of meaningful relationship whilst this is going on. It's ridiculous and most of all it's actually so so confusing for your children. They may love you being together but you aren't anymore and they need to be able to deal with that and come to terms with it. They will not understand if you are constantly acting like a couple.
Come on OP, separate your lives now. Let him move on with his girlfriend and stay out of it. You are coming across as the controlling one, you are the one who will confuse your children with this craziness.
Move on before you embarrass yourself further. The girlfriend has done absolutely nothing wrong here and I really hope your ex grows a spine and learns to say no to you from now on. Although you do sound like the type who'd start withholding access etc if things don't go your way, I hope not.