Should she be called Grandma, or no?

Ellie • Lauren Rozella-Mae 3.11.19 💖

Looking for honest opinions here. My Father-in-Law is getting re-married this October for the 3rd time to a woman he's only been dating for about 16 months or so (they got engaged shortly after dating for 1 year). We have only spent time with her maybe 5 or 6 times since she and my FIL started dating and both my husband and I feel like we barely know her. I'm very hesitant to allow her to be "grandma" to my daughter because we really don't know her, my FIL does not have a good track record with relationships and they decided to move out of state and will be spending their winters in Arizona. I'm confused because they are getting married so it seems like the right thing to do, but at the same time I barely know this woman and dont want to have to explain to my daughter why suddenly "grandma" is no longer around if something happens between them.