I've been following this thread with interest.
I think PPs saying OP is being mean to her mother & ought take care of her , given "pre- inheritance gift" have missed significant updates from OP, a clear legal view of situ and that it's Mother's behaviour that is causing the ructions to this plan ongoing.
The gift wasn't one with reservation of benefit. That would have needed to be legally annotated and it wasn't, or OP would have said. I understand PPs concern that Mother would struggle to buy a property without that money and more, depending on where in country they live (it's £220+k in my area), but she chose to give away an almost equal amount of money to her son too. OP's property would have risen in price regardless and it's difficult to know what an extension will add to future sale price, and a moot point when OP isn't selling anyway.
I'm not as unhopeful as others that this cannot be resolved or improved by some straight talking. Mother hasn't had bottom line laid out for her. She would be able to go on Housing waiting list for sheltered accomodation, if she has no funds to purchase a property with, legally not morally, so unless she's kept a hundred thousand or so in her bank, she is where she is. Hence, if it becomes untenable, then an alternative has to be found. There's a marked difference between giving away money & fairly quickly ask for rented housing association accomodation and housing benefit help, compared to capacitated gifts after death of a parent (his inheritance) with 4 years accomodation & live in support provided, whilst she needed it at a very vulnerable time. I'm not saying that'd cost £80k but it was Mother's choice to have extension for her to stay there. It's unlikely she stipulated how long and would likely have signed it as a gift for money laundering purposes, leaving herself no future claim.
I think Mother is acting somewhat entitled and hopefully that will resolve with a 3 way chat. If Mother is a bit more amenable now, she might find that care support she was hoping for in her twilight years is still on offer. She's being very silly to risk that, to make unnecessary jibes at OP now.