I'm also a divorced Mother with 3 sons. I've been remarried, but too young at the time to have stepgrandchildren by marriage, let alone stepchildren.
Are you asking about having stepgrandchildren through marriage to a new husband?
or stepgrandchildren through your children's remarriage to someone who had children?
I have a stepgrandchild, though I call him my grandson. He's 9 but I've only known him for 2 years though it feels like always. Our relationship is still growing - his mother (my son's wife) has made the door open, but she's like that -- she tries to include everyone and has a positive attitude toward his father's family, my son's father and family and my family. I would like to be more involved with him but I'm aware that he has a very busy life - and a lot of people and his own little life. So I am appreciative of the time I have with him and am trying to find things we have in common, and to make sure I'm not seen as competing with the grandparents who have known him since birth. But I consider him my grandson, that's how I introduce him to people.
I would think a lot of this would depend on the attitude of the children's parents, their relationship with their parent's new spouse, the absence or presence of other grandparents and their health and willingness to share the child, as well as the new stepgrandparent's wish to be involved in the life of the grandchildren. And of course the feeling of the grandchildren, too. A lot probably depends on their need for grandparents, the chemistry, their age, etc.
I don't think it is simple.