If you haven't told the children he is dying (let's call a spade a spade, that's what terminal illness is), should you now do so? I'm not saying it's a good idea, I'm saying it might be a good idea, so think about it. We are all brought up (as much by our peers as our parents) to believe that life should be "fair". As we get older we learn that it's anything but fair, and it can be a very hard lesson to learn. Perhaps your children are learning now, and, worse, blaming themselves for what is happening - illogically blaming, of course, but logic is never plentiful in these situations. We live in a world where there is a culture of blame - and the media always seem more concerned with pointing a finger than finding solutions. Cancer is a terrorist. It has no respect for age or lifestyle but attacks at random. It's like being in the wrong place at the wrong time and blame doesn't enter into it.
My wife and I are retired, and I am coping at present with her care. I don't think I could manage if I had three children to think of, too, as you have. Is it possible to get the children to help? (Here again, I'm just suggesting; it might work in some cases but not yours or might be a lousy idea anyway.) You're all in it together, and doing something positive might focus their minds differently. As a parent and grandparent, I know how difficult it is to accept that our sprogs grow up. Yours are approaching adulthood (although there is some way yet to go), and if you take them into your confidence, share your feelings (to some extent), and discuss with them what the four of you can do "as a team", you might be pleasantly surprised. However you know yourself and your children better than I do, so trust your own judgment on this!
My wife was fit and healthy until in April a severe pain and fainting made me call an ambulance. The following day she had a major operation and we were told that she had cancer which had spread. This week they confirmed our worse fears that it is terminal, but it has not yet fully sunk in to me. It seems possible that you are well and truly in shock, and if you have the time and haven't done so already, a trip to your GP to discuss yourself could help. There may not be anything practical, but even a chat should help and will do no harm.
Whatever, I wish you well.