Brought up on poor council estate in the north east and it was mostly Mam, but plenty of people used Mother too, but where I lived it was judged as common, with Mum and mummy being the wanky snobby label.
Youd hear people ( it always seemed to be men or boys thinking on it) shout "mother, passus me a, b c" or "mother fetch me this" and it would just sound so disrespectful, maybe it's the context it was used, always before an order or request.
My brother is lovely but is different to the breast of my immediate family in a way, in that he seems uncomfortable of how we were brought up, family can laugh at something for childhood and you can see his brain ticking thinking "omg, I'm so glad my DC won't experience that" and unless you knew him, he can come across as forgetting where he's from, or being ashamed but it's not. It's wanting to leave behind the shitty attitudes and judging and comments and bullying we had as a children from children and adults of "better" families.
When he was about 11 he tried to start calling Mam, Mum like the better of DC did and while my Mam didn't like it, she knew he wasn't snubbing her, he was just trying to keep his head down and avoid another beating from kids at school. He quickly realised that it didn't change anything though, they found something else.
If my Mam changed her title to whatever, I'd probably take the piss a bit, like I would about her posh telephone voice, I'm guilty of the same, I iften type Mum instead of Mam, and it's been a struggle to not go back and change it on this thread, I drop my "Geordie" accent for important phone calls, because for me, I feel taken more seriously when it's not assumed I'm "rough".
I'm absolutely not ashamed of my upbringing, or my life now (still council estate, not comfortable and I struggle with money still, but not breadline like when a child) but I'm careful about who I talk about it too because some people still hear the words "council estate" and judge.
If you family have had rough time growing up, could the title Mother be one of the few "posh" things she's been given, so she's adopted it? Could she be going along with it for your sister? Like my Mam did for my db? Could she feel correcting sister is pointing out her different life now and feel like she'd be pushing her away? It's something you need to talk about if it's upsetting you, just don't make it a one sister versus another sister thing? My Mam wouldn't correct me calling her Mam if one if the others decided to call her Mother, she wouldn't correct them either, so unless she is insisting you use Mother too, you can't really tell her to force others to use words you want, or use them herself. I do see why you feel upset though.
Whatsapp, my Mam everyday leaves message in our group chat contains all siblings and their partners/spouses with a "morning shitheads" and "goodnight cunts" :)