You categorized "Mum" and "Mummy" as British English and "Mom" and "Mommy" as North American. It's not quite that simple. I grew up in the U.S. but have lived in Canada for many years and I've heard a mix of all of these pronunciations here. "Mom" is the most common, but it's not at all unusual to hear "Mum" here. In fact, I was kind of surprised when I was in the hospital and the nurse handed me my first child saying "here you go, Mum!".
It is probably a regional thing; just like the U.S., Canada is a very big country. I live in eastern Ontario, where a lot of people here are just a few generations away from British ancestors. In general, people here sound mostly like Americans, but every so often you hear a different word (like "Mum") or a different vowel sound (like the Ontario "out", which is more like "eh-oot") and it reminds you you're in a different country.