I would see if you can hire a lightweight mobility scooter whilst on holiday.
Once you discover if that is actually possible - then have a conversation with your mum, and be honest with her, that you are upset she is missing out, you are frustrated that you want to spend time with her but are struggling to do so.
Then tell her, most people find it hard to transition to using a mobility aid, but pretty much everyone who does, finds that it does improve their quality of life - and she has the PERFECT opportunity to try it out, on holiday, where no one she knows will see her, and she won't see these people ever again either! She's totally anonymous!
I would lay it on a bit thick and really ask her to try it, for your sake if not for hers (I mean, really it is still for her sake but put it that way if you have to).
I absolutely get not wanting to be pushed around in a wheelchair, its horrible, I hated the idea when I first needed a manual chair, I hate it now and haven't used a manual chair for a few years (power chair now) - being under my own steam was MASSIVELY important to me and it is to most people tbh.