I have no words. It happened so quickly. I am sorry you were not able to be there with him in his final breaths, but I am so glad you were able to be there for him in the ways he needed you most over the last 35 days. He went out on his own terms.
I was young when my dad died, of a fast moving cancer, as well. If I can give any advice to you, as mom....let your kids see you cry, let them see you in your weak moments, and talk about dad as much as you can, and at any time they want. My mom, right after the funeral for her love of 35+ years, became a different person who, for all intents and purposes, "forgot" about my dad. It was very hard to not have my other parent to walk this journey with. I wanted her to be weak with me, to cry with me, to heal with me. It would have HELPED me to see her as miserable as I was. I wouldn't have felt so alone, or that I was taking too long to heal.
Strength doesn't just mean being the super-hero...it means being the person who others can come to because they know you will understand. It is people bonding together to heal after a tragedy. It is surviving, even when that is the last thing you want to do. You do not need to be the super-hero for your kids to heal. You will just need to be there, to hold their hand, to cry, to remember, to memorialize. And, there is no timeline...none at all. I am 18.5 years out from losing my dad, and I still have the weakest moments. The next days/months/year are going to be a blur. And that is ok.
Peace to you and yours, Rodeo. I am so very, very sorry for your loss.