Some people's opinions are led by their mood and emotions at the time.....but other people's emotions and behaviour is led by their opinions and thoughts.
Therefore, this could be less a case of someone being unpleasant because they're in a bad mood or in pain, and more about what they think they're justified in being annoyed about. If they think they're justified, then this results in anger and them behaving horribly.
Therefore, therapy or him not feeling any pain anymore may not work for him, because his behaviour being fuelled by deep seated opinions and personality traits that are difficult if not impossible to change.
I definitely understand why you and you're children have tried to comfort him. This is a totally normal, caring response and you're also trying to make things less unpleasant for yourselves. However, there doesn't seem much of a point with him.
You could even be fuelling his behaviour. What he's learning is -
I'm a dickhead to my family = I get attention, they all start tip-toeing around me, they all want to please me, they fawn on me.
This is not something to reinforce. It put you in a position of emotional servitude. I speak from experience and I didn't realise it was going on for such a long time because I trusted my ex.
It's complicated with children, but try this. The next time you even get a whiff of him starting to snap, take yourself and the kids away to another room if you can. If you're in the middle of having dinner and if you have a car, have the dinner in the car and lock the door until you're done. I'm serious. Deny him an audience, of your company, and leave him to stew in his own juices.