How about just Nan? Granny? Granna, Gran? But as a PP said your mum can still be just Nanna and if your MIL wants to be Nanna too, then your kids will just need to add her name to the end of it. But it's your MILs choice and it would be rude of you to suggest perhaps she use something else. You could just be worrying for nothing.
Is your MIL ethnic at all? My dad chose Popou which is Greek for Pappa and my mum chose Granny. They hardly go together but that's what they chose. FIL chose Granda!