I know this isn’t the advice you asked for, but my DGM refused to use a wheelchair until I hired one for a holiday “just in case” - just to try it and see, so she didn’t have to miss out - and it was a bit of a revelation for her. Once she’d gotten over the mental block of sitting in it she realised it was great - she could go round shops, into pubs, nice walks etc. As soon as we got home she bought one. The woman at the mobility aids shop said it was really common for people to be horrified of the prospect and steadfastly refuse to entertain the notion, but then when they end up trying it out they realise how beneficial they are.
DGM was a very proud woman, always beautifully turned out and a heck of a character - she used to hold her walking stick like a lance and have me push her at a run, and god forbid if you didn’t follow her directions 😆. But my point is that after a lot of swearing and muttering and moaning, once she tried a wheelchair she never looked back, and we had fun.
Anyhow, perhaps it might be worth trying - present is as a fait accompli, as in “I’ve hired this so you don’t miss any of the fun, it’ll be in the boot of the car, just say if you want to give it a try”. Or, “Mum, there’s a lovely walk with a smashing tea room/pub/whatever at the end, so let’s give it a whirl and see how it goes”.
I can totally understand you feeling frustrated and irritated with your DM, but using mobility aids for some people is like an admission of frailty, it must be scary and upsetting to face the reality of an aging body. It’s awkward because it’s not something you can, or should, try to force her into - but if you can somehow encourage her to come to an acceptance of it as something that will enhance her quality of life (rather than a badge of frailty) then it might help? Easier said than done though!