How am I able to seek help to determine if my mother (71) has a personality disorder, dementia, just being mean or is it me?

My father passed many years ago and my mother hasn’t been the same since. Yet she and I have always bumbled along. After my Great Aunt’s death last year, (I organised the funeral and packed up the house), Now it’s just us in the family and I live overseas but Mum is at home. She has been to visit for three months and it’s been torturous. She has been mean to me most days, and when I challenge her to respect me, my home, my boundaries, I feel like it’s me being the unreasonable one. E.g, I invited her to my work Christmas party today. She had a few weeks notice and wanted to come. After some mean comments which I ignored, (she stood me up when I organised a weekend away - then she said she would come back and visit those places with friends) - I asked her to be nice and could we please be calm before the event as it was important to me. She agreed. Ten mins later whilst I’m sending my godson his Christmas gift at the post office, I ask her if she wouldn’t mind buying me some small chips in the shop next door (as I hadn’t eaten all day) before we head home to get ready for party/bbq. I send my parcel then wonder where she is. I return to find her sitting at a table in the cafe with a big gourmet burger on a plate in front of her, coke and chips. I explode - I behaved horribly - completely upset - asking - why did you order a meal? We have to go. We are going to a bbq?! Why would you order a meal before a bbq? Of course not food for me either. Notably she says I didn’t think you wanted me to come. (We planned it for weeks and spoke about it ten mins before) she says - It was a meal offer so I bought it. She goes to the counter - tells the waitress - she isn’t happy with me - she wants me to pack it up. The waitress looks horrified at me. I offer to reimburse my mother but we have to go. We end up binning the burger. I feel horrendous - not only about my own reaction - but don’t understand. Like so many things, we plan a few weeks in advance (like buying a Christmas tree/decorations in my new home) then when the event approaches she sabotages it, ruins the moment (says let me help with the lights then says Christmas trees are a waste of time as we begin to put the lights on).

But why would she be like this? Am I being the bad daughter? I’ve been through so much and this behaviour is just too much. She calls me fat in front of friends, says (oh look at you being so articulate whilst I’m talking to colleagues) Is it age? Mean streak? It only seems to be me that she is mean to - but how would I know? And she is so nice in public.

It’s just me to care for her and I really don’t know what to do. Do I need to give up my life to go home to care for her?