First of all, it has been very confusing at my parents house because my mother refers to my grandma as 'grandma' (my grandmother lives with my parents) and I have been referring to my mother as Alex's 'grandma'. So when I talk about 'grandma' mom thinks I'm talking about Alex's great-grandma; and when my mom talks about 'grandma' I think she is talking about herself, but in fact, she is talking about my grandma. Confusing I know.
I've suggested that we refer to Alex's great-grandma as 'obachan' (Japanese for grandma - what little children call their grandmother in Japanese) as that is what I called my great-grandmother. However, my mom has decided that 'grandma' will stay 'grandma' and she will be called Nana.
mother