The role of a step parent in the life of a child after the parent dies is an area where there is little remedy, much to the unhappiness of some step-parents and step-children who have built a relationship with each other only to find that relationship goes largely unrecognized by courts.
In most cases when one of divorced parents dies, the remaining parent assumes full custody of the child or children and the opportunity for the widowed step parent to see the children depends on the willingness of the remaining parent (which is obviously complicated, even in amicable divorces).
But there are legal ways around it.
Need to take your stepchild to the doctor? Have both parents sign a form. File it with the doctor, and carry one on you. Keep in mind that no emergency department will refuse treatment to a child just because their parents aren't there. Just check the doctor's policy first. My stepson has one doctor that requires a new note signed by one parent for every visit, specifying the date.
You can sign some things for the school, like that you reviewed homework or an exam or something. Anyone can do that. It's not a legal document. But if it's a class trip or some other legal form, just have your spouse sign it.
You can't sign releases for sports or things like that, but after the initial one is signed, send in another letter allowing others to act in the event that a parent cannot be contacted.
Schools usually have spaces where a parent can designate others to pick up their kid or receive information. Make sure your name is on that form.
Between grandparents and stepparents, there are plenty of people who are the primary caregivers of children who are not legally theirs.
I'm the primary caregiver to my stepson.
Wednesday, I have to take him for an eye exam. I have a form signed by both his parents allowing me to bring him in for a regular check-up. They'll check his vision, but if they wanted to advise something extra (like dilation or something), they wouldn't let me authorize it. He also has baseball twice this week. I didn't sign the waiver for participation (that was my husband), but there's nothing illegal about being the one who brings him to practice.
Of course, this is a lot easier considering that all three of us are on the same page about this. If we need both parents' signatures, it's not a problem.