Complicated family situation.
On holiday last year, I pointed out to a relative (she is married to a blood relative) that she was being rude to waiting staff. I had endured a week of it and I was totally exasperated. She's very outspoken and ready with her criticism of everyone, so I thought in that context it was OK to speak out. Anyway, it didn't go well. She just started to shout at me at the dinner table. She is non English and often criticises the English for being uptight, conservative, capable of only small talk, dull, forming ridiculous queues etc. Anyway, as she started to shout at me, I gently suggested that the way she behaved with waiters might be acceptable in her home country but it was considered impolite in the UK. I said that to offer her some form 'get out' for her horrible behaviour, actually in an attempt to defuse the situation. But she just carried on shouting at me then left the table in a huffy. And left the holiday without saying goodbye to me, my husband or my children. Her husband and children came to say goodbye to us as they left but not her. We just chuckled about it.
We have since hosted various large family gatherings and have invited her along with her husband and her children, but her husband and children have attended alone.
Her husband has today been in touch to say she is refusing to attend a forthcoming family gathering at a restaurant unless she receives an apology for the incident last summer. Her husband said he thinks she's being unreasonable. I've asked my husband if he feels I should apologise. (He was present.) He doesn't think I have anything to apologise for. Her husband said she will give him a hard time if he attends the gathering without her, and as he'd like to attend he has contacted us looking for a resolution. I think he's used to subordinating to her, so probably thinks we will do likewise.
I don't feel I did anything wrong. And most certainly not in the context of the way she dishes out outspoken criticism to others. But I do now wish I hadn't said what I said. 
It's nothing short of astonishing that she's reacted in such a prickly manner and is attempting to paint herself as some sort of victim. If anything I feel she owes me an apology. We have assured the husband that as far as we're concerned it's all water under the carpet and we have demonstrated our white flag by inviting her to our home on a few occasions.
Do you think I should apologise? I could and would if I felt it was the right thing to do.
Or should we just offer not to go to the gathering, so they can go together?
Or do we just ignore their nonsense and attend. And let them decide themselves whether to attend or not attend? It's such a lot of nonsense. I feel embarrassed to have written this down.