Slow down, and do things in a sensible order 
I posted a lot on a previous thread about your mortgage and this guy.
Did you ever find out if your XH added £100K to your mortgage by forging your signature? Or did you just sign the remortgage?
That was only 18 months ago, so you'd been with this boyfriend 9 months without having the terms of your split sorted out.
SLOW DOWN.
Where's the fire?
You have no good reason to move from your current house, from what you've posted. So what if it was the marital home? You've had long enough with your new boyfriend there to build new memories of it now anyway.
Why not wait another 2 years until he has paid off his DMP, you can get lower interest rates, and you might actually feel sure of his commitment?
(by the way, it's 2016, you're allowed to propose)
But look, this is my big concern for you...
You can't get a mortgage on your own.
When you were married, you relied on your husband's come.
When you divorced, you relied on him staying on the mortgage.
Now you're relying on another man to get you out of the mortgage tie with your husband.
this is a big mistake
At the moment, you own your own home with all the security and appreciating asset of that. Yes, you only do so because XH is on the mortgage but you have protection. Your XH had a good reason to go along with that - it is housing his child.
Now, say you and DMP Boy split up. You've ditched the security of your XH having to keep you in the house by staying on the mortgage. DMP Boy will want his money out. Now let's say that actually you were sensible - not married, and your split is protected. So - you only need to buy him out a "fair" amount.
But guess what? You can't. Because you still can't get a mortgage on your own.
But this time, tough shit - no way is DMP Boy going to stay on your mortgage stopping him from getting another one. Your kids aren't his problem.
So you end up with a big old chunk of equity - but no ability to get a mortgage on your own that will allow you to keep your current home. And if you're in an expensive area, even downsizing wouldn't be an option.
You would be an absolute fool to give up the mortgage that you have, with your XH on it, until you (not you and DMP Boy) can afford to take it on.