Hi Daughter#2, welcome to TP
I had to put up with not being recognised for a while, me and the "other" people in the house (who don't actually exist), it went on for a while but did stop.
To cope every time I wasn't recognised and started to kick off I offered her something nice like a biscuit, cup of tea, cigarette anything to distract her. Eventually she came to see me as someone she liked although she'd didn't and still hasn't any real idea who I am, what I'm called or what our relationship is, currently I'm being called by her oldest brother's name.
I would say that people take this happening differently, some are devastated that they're no longer recognised and take it deeply and personally, I was aware this might happen and although it's not what anyone would want I can accept it's one of the things that may happen and in my case did so I don't take it personally.
The "other" people that lived in the house turned out to be reflections in the mirrors, we have several and when she saw her or my reflection she perceived it to be another, different person, she couldn't even recognise her own reflection and wanted "that woman" out of our house, in the end I took them down and I've noticed that the EMI care homes I've been in don't have mirrors either.
On here we say that "you have to live in their world because they can't live in ours" and it's true, your mum's reality is every bit as real to her as our reality is to us so there's little point in correcting.
Last bit, "Anyone had a similar problem? " yes, loads of people on here have, it's really very common for this to happen and can be very difficult to deal with.
K