I am so very sorry to hear of your loss. My mum lost her very best friend a few weeks ago - we found out her cancer had come back (in her liver) on the Tuesday evening, planned to visit her on the Wednesday, but at 5.50am Wednesday morning she was gone!
Such a horrible shock, but I know this: although cancer took her far too early, she really did have her own way... the lovely lady we lost never wanted to be in extended pain, or for her family to watch her deteriorate and die slowly. She didn't have long to spend suffering, or to be frightened of what was to come. It's just VERY difficult for those left behind. You probably feel robbed of 10/20/30 years - but years spent in suffering and worry are not years we would want for those we love.
As so many others have said, I think the best thing is to immerse yourself in your wonderful boys. I'm sure when you look into their eyes you will see yourself at times? Well, your mum is there inside you in just the very same way - we mothers leave an indelible mark on our children, and I'm sure that will come through and you will touch your own children's hearts the same way she has touched yours.
Every memory you have of her, write it down and keep it in a special book with favourite photos of her in it. A story she used to tell, a daft habit she had, a joke she always got wrong, special times you spent together... This will be something precious to keep and something your boys can enjoy when they are older.
I'm so sorry this had to happen, but I hope that each day heals your hurt a little more. I will be thinking of you and will include you and your family in my prayers. xx