Hmm. These are my thoughts.
Firstly, there’s quite a lot of “he shouldn’t be putting his children before you” thoughts here. Well no, except they are his children and on another thread (about childcare) you’ll see some of the same people saying your partner shouldn’t be dictating how you deal with your family, it’s up to you.
Maybe he is “putting them first”. Ask yourself honestly if you would be prepared to lose your children in order to do what your partner wanted.
From his children’s point of view why should you have shares in a house that their parents worked for together?
If he made over a share to you would you be happy for his children to have an equal share in your house?
A viewpoint depends on where you are standing, doesn’t it?
So assuming you want to stay with him, he wants to stay in the house. Is there a way to be happy?
Maybe not. But many, many people live in a house that they do not own, the bricks and mortar. It’s called renting. They live their all their lives and for them it is home because they have made it home. A place where they belong. Is there any way of belonging?
Can I suggest that wanting to involve you in the extension is his way of getting you to feel that the house is yours, both of you. A project that you are doing together to make a home.
Can you ask yourself why actually owning, having a financial interest, is so important to you?
I am in a similar position to you, actually, and after living independently for some years. I’m having to come to the realisation now that I can no longer have my home (and I do consider it home) just they way I want. I’m having to compromise, live with furniture I don’t like, negotiate changes. It’s tough, but worth it. And probably very good for me?
I hope you can find a way to be happy?