He isn't after the company, sounds like he just wants a housekeeper (you)
THIS ^
In all seriousness, even if you and he were very fond of each other, and had interests in common (I dunno? - collecting walking sticks?) and he was a very capable man around he house who would have a nice lasagne ready for you when you came in from work etch would say DON'T DO IT!
It will completely alter the dynamics of ALL the family relationships.
There will soon be friction between the two of you and that will cause a conflict of interest between you and DH.
He will get annoyed with your children for being children (if he's no a sociable person, I can't see him being happy with the noise and mess that all children cause, no matter what their ages).
He will feel that because he has given you half the value of his house, that he has a "right" to behave how he wants to in YOUR home.
He will interfere in your relationships - with DH, withs DCs, with friends and other family (the last is inevitable if you will no longer have a spare room for guests).
He will complain that you don't do things the way his wife used to (he will - he sounds a really selfish prick, forcing a terminally ill woman to look after him, and not even learning how to cook a few basic dishes,) and he will take those complaints to your DH.
He will want to go on holiday with you, or will complain bitterly that you leave him alone at home.
You will get no respite and it will ruin your life (not being over-dramatic here). You will end up HATING him, and it will spoil your children's social lives too.
Your suggestion that he moves to live near, and you have him round for dinner a few evenings a week is a very generous one. Or he could move himself into sheltered accommodation. That way he will be able to have his privacy and own home within the complex, while also having access to facilities for food etc whenever he wanted them.