I don't want to give too much detail here, can't afford to give too much away really.
I have a child in your DS's position, though several years younger. I too have told her that it doesn't bother me in the slightest. It changes nothing with regard to how I love her and how proud I am of her. I think they need to hear that, so I think you reacted in exactly the right way. It is good that your DS now knows that he can count on you.
I am not certain how my DH would react, and nor is my child. He doesn't have the anger management issues that you suggest yours has, but he can be tactless in the extreme - mouth into gear and then think/ask questions later. I have discussed it with my child as she is nervous of how it would go, plus the fact that she has had related mental health issues in the past. She is in agreement that for now we just leave him to work it out himself over time because his potential reaction is not something she yet feels able to face. It is the right approach for us.
I know my DH loves all of our children unconditionally, but I also have vast experience of dealing with his tactless tendencies.
I am sorry to hear about your father too. It is clearly a very difficult time for you. My MIL died from advanced lung cancer in May 2014 and it was painful for the whole family. You have my every sympathy.
On perhaps a more positive note, I wish you well for your new job and hope it goes smoothly. You need a bit of luck right now.