When you married him were they already adults?
Has your husband ever spoken to them about how he feels?
Do you get along with them otherwise?
Do the two of you have any children together?
What have you done to change their mind about you in 13 yrs?
Has there been issues or just dismissive things like asking you to step out of the pictures?
Although he is ill, can he not speak up and say "she is family, I want her in the picture"?
It seems that the children's selfishness extends beyond just you, and to their father as well. So at least you know it's not you. If the only thing they care about was his money, its possible they were not raised with the best values about love and money and now that is showing in how they are treating him now. Many people equate love with money, its not uncommon to see this in children who have been spoiled.
I would say to continue doing what you do for the grandchildren, as it's not their fault how their parents act. As for his children, 13 years is about long enough to cater to someone for love or respect. You are well within your rights to live your life and not be obligated to them in any way. Your husband chose to marry you, and you chose to marry him. His children are adults and capable of making their own decision and if they don't want to be cordial to you, then you stay a lady, be polite, but don't go overboard. Don't overextend yourself for anyone anymore thats not willing to do the same for you. They have proven after all this time that they don't care about making you miserable, and enough is enough. Take the attention and energy that you put toward them, and put it into your husband and your marriage.
I welcome your thoughts, let me know if you want to talk more.
ps. make sure that you and his will is in order in case something should happen to either of you, both of your wishes are in black and white and cannot be disputed by the children