My condolences on your loss.
I have to say, DH has had a couple of inheritances (5 figures) and what he has done with it has been his decision. Likewise, in time, if I inherit anything from my Dm, I would consider it my money. Not to say that we haven't /wouldn't spend money on the house, children etc, but ultimately that person's decision. I could never consider his inheritance "my" money.
I was wondering if you would be able to work? With another full time salary you could pay off your mortgage much quicker, plus save for repairs. Of course I appreciate you may have health issues preventing you from doing so, but if you can, this would give you a lot more security in your financial situation, and perhaps you wouldn't view his inheritance as a "way out" of the house issues.
With regards to money to the children, and hi potential differing feelings towards the children, what does it state in your wills?
These things usually take some time to resolve, so give him time, allow him to grieve, and keep the communication open.