My situation was similar to yours, 3 kids, diagnosed at 39, and ignored symptoms that I didn't realize were symptoms.
I know it's overwhelming in the beginning, how you go from being fine one day to being a cancer patient the next. My kids have been very understanding, but it has been a rollercoaster for them. The initial diagnosis was easy for them because they believed me when I said I wasn't going to die. They had a harder time seeing the "proof" that I was sick - first the PICC line and the pump, then being in the hospital, and then seeing me get sick from the chemo. Each time I had to reassure them that the cancer was better (or gone), but it was the medicine making me sick, and that it was temporary.
One of my daughters is a worrier. On occasion, she would start to stress about my condition, so we took her to see a friend of mine who is a therapist. She recommended the following things to help her cope with me being sick:
1. Getting a "Mommy pillow" for her to help her at nighttime, when her anxiety is especially strong. We ordered a pillow with a picture of us together on it. You can even spray it with your perfume if you wear any.
2. Give her a list of things she can do to make you feel better. It helps feel empowered. My list includes making me a smoothie and reading a story to her brother.
3. Journal her feelings, or draw pictures of what she pictures in her head when she gets worried.
Hope this helps.