I can see why you would feel marriage would give you more "security". But - as you found with your first marriage - it doesn't, really. It just gives someone else legal rights over your assets and your cash.
Honestly, now you're a mum with a hugely valuable financial asset, you need to start thinking like a businesswoman. Not like a lovestruck young girl.
Make a list of everything you need: help with the house, childcare, £100k for the ex, a certain amount if money every month, a house for you to live in with your kids short-term, and an inheritance for them long-term. Then think PRACTICALLY about how you can achieve those things. Is it marriage to THIS man? It doesn't sound like it. Is it living alone but with a housekeeper, an au pair, another person (who won't activate your ex's charge on the house)?
Please don't argue with your own solicitor! They have NO reason to warn you off this marriage except that it's not in your best interests yet. In the future, when your ex is paid off and maybe you've sold the house and put some of the money into trusts for your kids (for example), it might be. But right now it's not. It won't give you financial security, help at home, protect your kids or get rid of your ex. In most logical terms, marriage right now is pointless.
Have a party or a blessing or some hand-tying celebration in a field if you want to cement your love, but please please please don't give all your cash away! Not now. Not yet.
Why are you so stubborn about this?! Is your DP really pushing for it? If he is, don't dall into the trap of thinking that's really romantic and a sign of his true, eternal love. Honestly - a man who loves a woman generally just wants to live with her all the time. Let him work out the logistics of that to show you how keen he is.