This is an interesting topic. On the grandparent issue first: My sister had the first of my mother's grandchildren, 10 years before I gave birth to my first daughter. Anyway, she decided to have my nephew call my mother "Nani". So, after I had my oldest, I was - of course - going to stick with what my sister had started off with 10 years before, and would point at my mother and say "Nani". Well, my daughter had other ideas! When Zoe was around 1, and beginning to talk, I left her with my mother for the evening. Mother and Zoe were on the floor playing and Zoe pointed at mother and said, rather emphatically, "MAM-MAM!". When I returned from the evening out, my mother informed me that Zoe had changed her name. Now, not only do my two daughters call her "Mam-Mam", but my
other sister, when she got around to having kids, too, has had her's call my mother "Mam-Mam", as well. So, now all the grandchildren except my nephew Carl calls my mother "Mam-Mam", while he - now 21 - still calls her "Nani".
We called my grandparents "Mom and Pop". This was due to my mother wanting her children to be proper and call them "Grandmother and Grandfather". But - surprise, surprise - that was very difficult to say; so, my grandmother said, "I'll turn them into 'Frenchies'" (she spoke 5 languages fluently, French was just one of them, and she was part-French). She tried to get Jayelynn (my oldest sister - there is 18 years between us) to say "Ma-ma" (accent on the last "ma") and "Pa-pa" (again, accent on the latter "pa"), but what Jayelynn ended up saying was "Pop-Pop". In the end, the second "Pop" was dropped and "Ma-Ma" just never took off - it was always "Mom". Since our grandmother was "Mom", our mother - of necessity - never was; she has always been refered to as "Mommy" or "Mother".
Now, as for me...I suppose the sweet little one I carry now will call me "Mum" or "Mummy", and this is peachy with me. Whilst, I am sure, my American kids will always call me "Mommy" and "Mom". It's all good.
As long as they remember to say "I love you" now and then - and mean it - I don't care if it's a "u" or an "o" sound between the "m's".