My dad's parents are Nana and Pawpaw to me. My mom's parents were a little upset about it as that's what they were already called by other grandchildren. They stayed Nana and Papa (different spelling) to their other grandchildren, but to me and my brother they became Nanny and Papa C (C is the initial of their last name).

Maybe that would work in your situation -- other grandchildren (if she has or will have) can call her Mom-mom, but your kids could call her something else.