Does my mother have grandparents' rights? Military family involved..?

Long story short, my mother isn't able to see her granddaughter. Her daughter (my sister) refuses to let her see the baby, she is crazy and thinks our mother wants to steal her baby. Which, in reality, someone SHOULD, because she doesn't take care of her 8-month-old. She went as low as to put a restraining order on our mother in which she falsely accused her of abusing her, but the judge thought she was an idiot and dropped those charges thankfully. My mother would like to be able to see the baby now and again to know that she is okay. They are in Florida now. Mom took care of that baby (my sister never touched the baby) for 3 months straight, if that matters. I believe FL has grandparent's rights, but my sister is married to an abusive soldier (she won't tell police, she doesn't want to leave him, then she would have to live with mom and go by rules, she'd rather endanger her child), what if they get sent somewhere overseas? Then what hope does my mother have in seeing her granddaughter? What about when they move out of Florida in general? She just wants to be able to make sure the baby is okay, but my sister is absolutely psychotic and hates our mother beyond all belief, for no reason (other than that mom tried to enforce rules, which is what parents do-she's just severely rebellious).