Until my son ended his marriage, I was a fully-fledged honorary grandmother to his step-children and treated them the same as my grandson, especially because their paternal grandparents were off the scene (I now know why - ex-dIL alienated them in the same way she treated my son's family). The eldest step-daughter felt so attached to my son, who helped her financially and brought her back home when she got pregnant, that she changed her surname to his by deed poll, and still keeps his name. He continued to help her months after he left, despite his business going downhill when he was too distressed to work because he was not allowed to see his son. She has torn loyalties now. Her mother will not tolerate any attempt to speak to me or my son (although the step-children are all in touch with him and support his decision to leave their mother).
If the strength of feeling between 'grandmothers' and the step-grandchildren is a gauge, I would say it is not genes that determine whether you should be called grandmother, but the relationship. It doesn't confer any rights, and even if you earn the position, it can be broken by a parent for all sorts of reasons. If you can rescue the relationship, I would say do what you can. I'm not sure whether them knowing how hurt you are will swing it - that tells them it's all about you, and maybe a little humility will bring a change. That's not to decry your feelngs - I can imagne just how hurt you are, but experience tells me your hurt feelings aren't their priority right now.
.......and if the children are enjoying a good relationship with the other 'grandmother' how fantastic that there are more loving adults around them.