Honestly, it's not problem, if I can help I will.
How much equity is in the property (pm me if you prefer).
The mortgage company didn't want a agents valuation, they just wanted to ensure that the asset they were borrowing against could repay the debt in worse case scenario. They do not care about emotions, they just want assurances their money is safe.
The debt, is now absorbed into the mortgage, essentially it doesn't exist, anywhere but in your mortgage, but that doesn't mean you can't use it as a bargaining tool. Call the bluff, I did. God knows I did what ever was necessary. You could always put through a proposal to him, based on the average of the 50% equity across three agent valuations, then deduct his £30k essentially writing off any interest.
You can essentially negotiate anything you want. You could say 30% now and 20% when you remortgage in 5years. There's lots you can consider.
If you can raise any funds now, you could lock him in now, until the flat is sold. In my experience, the more time that passes the harder it gets. Anything you agree now, needs to be legally binding. I spent a fortune on legal fees that I hadn't factored in. My ex chose not to take legal advice, despite me paying for his solicitor.
In your shoes, I would get three market valuations, get a mortgage valuation (go though the process to get it started and get the other flat on the market asap). Get the ball rolling.
Yes, the childrens act comes into play whether married or not. Children of unmarried couples are not less protected than those of married.
Could your family buy his 50% against the flat? So it can move quicker? So they remortgage the flat, release the funds and buy his share?