Some families do lifts and some don’t and I have observed that in the ones that do there is always an unequal partnership in that some family members make outrageous demands and the others fulfil them without being able to challenge the requests.
My DS has married into a family where lifts to airports, pickups and lifts can be any number of miles and at any time of the night or day. Some relatives will book cheap night flights to suit themselves in the certain knowledge that someone (who will have a demanding job and need to be rested) will picked them up in the early hours and take them home or give them a bed for the night.
Once, she asked if her DH could stay with us as he had to fly from our nearest airport, 25 minutes away and had to check in at five a.m. We said, yes, of course and also mentioned that, because of the proximity, there were many and cheap taxis available to take him there. (i was teaching that day and the OH had a nightmare commute for work.)
A very frosty silence ensued and the request withdrawn. Relations never really recovered.
IMHO, people know very well when they are making unreasonable requests and will usually sulk and make others miserable if these CF demands are not met.
In the case of the OP’s parent with whom she will not want to fall out, perhaps the situation is to make some reasonable caveat. She could say, ‘ In order not to sit in the car for a couple of hours since there is nothing to do in the village and no time to go elsewhere, perhaps I could join you both in the pub?’
Or just lie. Invent an excuse for that day. ‘I have root canal work booked for that time.’
I don’t think lying for one’s own benefit is moral or desirable but if others place you in a poor situation with moral blackmail you are, perhaps, entitled to defend yourself likewise.