I never really wanted to get married and blend families etc, and I made no secret of that. I was financially secure in my own home. He had less money to spare than me for various reasons, and it made sense for us to be no longer paying two mortgages etc. So we got married. His idea. I extended my house to make room for his kids to stay. But if I'm honest we haven't really been properly happy ever since.
You need to keep reading this, your first (honest) paragraph on this.
You were delicately bounced into marriage by a man who, while absolutely not a monster, does sound manipulative, a bit of a typical male user, and who definitely knows very, very well that he has struck it extremely lucky with finding a fairly compliant woman who will do most of the shitwork while also compromising her whole life and even her financial security to make his life nicer and better off.
He knows it. That's why he did it. If he'd been the higher earner with the bigger equity pot then you would not be married in a million years.
This thread has happened because now, two years down the line, he's beginning to relax into what he feels should be the dynamic: him as head of the household and entitled to direct where the ££ goes, and you as wifey (with associated wifeywork of course) and his kids as centred within the family - even over and above yours.
His mask slipped as a result and you have the situation with your DD.
'Constant arguments' 
Ok, what will happen now I can predict to the letter. He will be an absolute model husband. You think he doesn't know exactly how long this needs to go on for your marriage to be classed as no longer short term? You think he doesn't know that it doesn't matter now that you're married that his name isn't on the deeds to your house??
He will behave impeccably now.
It does not change a single word of your first paragraph, but what he's done is very clever, because naturally, you will think this:
I'm not keen to throw away a second marriage so soon.
WHY??? !! - when it's a marriage you didn't want and has not made you happy?!
If I were you I would get to the solicitors asap and have a very long conversation about exactly what you and your children stand to lose. It's not even about ultimate inheritance. Ask yourself if you are effectively going to find yourself in a position where you cannot afford to get rid of him down the line because half your house is yours and you can't afford to buy him out now it's a medium/long term marriage.
He has played you. You KNOW that in the simple words 'I didn't want to get married'. That means he manipulated you and knew how to do it. He is and will continue doing it now and he knows it.
Really really think because 'throwing away this marriage so soon' sounds to me EXACTLY what you should be doing.