I'm not sure there's anything for you to 'do' specifically happytalk - this crisis is really your kids', and it's for you to be the facilitator as best you can... which means running around really, listening, being there, doing all you can practically. Really it's for them to sort it out, bcs it is them who are losing their dad, and for you to be always on hand if they want it (they may not). They aren't little, even though they are still very young to be losing a parent. The one thing I would suggest is that you promote they see him and talk to him as much as possible in these last days.
My ex-h was killed about 18 months ago and that was sudden - my kids would have valued so much having some time to say goodbye. Your son says he isn't close to his dad, but he's his dad, and that will throw up a lot of strong feelings. The grief runs for quite a while esp as, although this isn't totally sudden, it is quite sudden iyswim ie the deterioration has been quick .
As someone said, don't forget you Sarah! Although I had been divorced from their dad for donkey's years, and loathed the man (it was mutual), I had some very confused feeling after he died. Tbh I grieved - for what was, I suppose? I still feel extremely sad about it, but how much that is for my kids I can't tell.
I'm afraid it's going to be a long road ahead - you can't hurry grief, and it goes in fits and starts. I may be wrong, but I think boys/men/males sit on grief and it comes out later. I'm still waiting for it to hit my boy (16) that his dad has gone, whereas at the mo it is really hitting my girl (19) and she is having a very wobbly time.
I would suggest they have as much to do with arrangements as possible to feel part of the process iyswim - they don't want to feel left out and irrelevant in their dad's life. IME my kids have been in full shock for at least the first year, then it gradually begins to seep through iyswim. I hope they have a good relationship with his partner, as that will help. Good luck hun X (sorry for long post)