OP do take legal advice on this with regards to the specifics of your situation because it all sounds risky and complicated. I appreciate your comments about the ill health in your family but if this goes wrong, it will add to your woes, not help them. I've listed some watchouts below which spring to mind.
Even if you just cohabit, he could, if he pays for home improvements or does DIY that adds to the value of the house, be considered to have a financial interest in the house. If you split you might find yourself paying him out. That's without marriage!
With marriage, you risk the house in the event of a divorce but you can look at ring fencing it prior to and in anticipation of the marriage.
Also as the non property owning spouse, he can register a Home Rights Notice on your house with Land Registry which prevents you from selling your home out from under him because it would be his home too. It doesn't implicitly give him a financial share of the home but it could be a troublesome spanner in the works for you until the divorce and financial settlement are through.
You can make a new will in anticipation of marriage (I believe a time limit applies) which would be valid after marriage but your current will would be null and void upon marriage and if you died before making a new will, you would be considered to have died intestate.
If you don't divorce ever but predecease him and leave the house to your 2 kids he could challenge your will. I'm not saying he'd necessarily be successful but the costs of defending your will against this challenge come out of your estate.
You can leave him with a life interest in the property so he had somewhere to live but you'd need to think about things like him forming a new relationship and his right to stay there and what to do if he doesn't look after the property and your asset devalues and becomes a liability/moneypit for your kids to sort. He could possibly ask them to leave when they're young adults.
Just to clarify as well, there's a difference between division of assets upon divorce and how your property is dealt with in the event of your death. Divorce starts with a 50/50 split with variations considered due to length of marriage/kids etc. In your will, you can leave anything you wholly own to whoever you like. That doesn't mean the will can't be challenged in court by a disinherited spouse but as said earlier it would, regardless of how successful or not they were, add cost to your estate, not to mention huge stress for your kids. Remember this man has nothing to lose and everything to gain.
Unless you can afford to rebuild your assets if it all went south I think you'd be taking too big a risk with your kids' home and security. At least consult with a lawyer so you know fully what the risks are and what you can do to minimise them if you do decide to go ahead. Make sure there is written evidence that your DP knows what the plans are so he is not blindsided by the protections you put on your property. Having said all that, his attitude to your house is already overly proprietorial, disrespectful and concerning. In your shoes, I would not be marrying or living with him.