"I find it odd that many British women are starting to believe ‘mom’ is a British word. "
This comes up a lot on here. It was taken to America around 1860. Middle English had Mome, but it meant Aunt, or older care giver female.
My Grandmother used Mam, her Mother had, her Mother was born in Liverpool, in the 1880's, they had Irish in their background.
I use Gotten, my Grandmother did and so does Maggie Smith, so it's good enough for me.
Two of my DDs have names and a middle name, which people think are American, but they are old English names and the middle name, which people think is a Unique spelling is the English version.
'American' evolved from the immigrants that took their language with them and then they all had to communicate. That included words which many think are American in origin, but were taken over there.