I originally read the thread as OP being stranded and her sister and family refusing to drive 20mins to help. That sounded very unreasonable.
However through all the obtuse drip feeding, it sounds like someone OP knows (a partner? boyfriend?) was stranded and she wanted family members to pick them up. Less unreasonable because we have no idea what the dynamics are.
Since OP is not forthcoming with any information, these are just some potential speculations:
Family might not approve of the partner and they know similar situations have happened before where OP needs to cater to his every whim. There are women who put their partner's needs above everyone else's and you can imagine getting a phone call at night asking you to be a taxi service to a boyfriend you may not even know.
Partner might be abusive or coercive and OP needed to "fix" the situation for him to prevent escalation.
Saying that a relationship with a sister is forever damaged because she didn't want to pick a partner up from the station is quite extreme. There must be lots more at stake that OP has not revealed.
It's pure coincidence that there were family members living in the vicinity. If the situation happened somewhere else then the partner would simply have to sleep in the station. Just like a missed flight. Such things happen to adults and is not the end of the world.
Note the usage of "partner" not husband which the family might know better. Nobody knows how well the family members in question know this man, or how many partners OP has had within context. If it's just the latest Tinder date then nobody should feel obliged to give him a lift from the station.