@Slomi
I think your idea to go, and 'show your face' and then leave early is a good idea.
I suffer from social anxiety, and hate social events with lots of people, and DH is very shy, but we don't want to appear rude and ungracious, especially as we sometimes enjoy it when we're there.
However, me and DH have been invited to five quite big events in the past 3 years, and on all but one event, we have not known anyone except the one person (or couple) who invited us. So we felt really awkward and left out. It was no-one's fault; it's just that people didn't know us, and we are too nervous and shy to start talking to lots of people we don't know. So we will often go somewhere, and leave after a couple of hours.
But no-one seems to mind; they are happy we came, and it's nice that they asked us.
Regarding your issue, I know it's nice to do things because 'it's important to your partner,' but it's a fine line between 'making your partner happy,' and ending up doing things you don't want to do, and are unhappy doing, because you feel bad for saying no, (or you partner makes you feel bad for saying no.)
I had a boyfriend some many years ago, when I was very young, who he was always going to see his mates, sometimes 2 or 3 times a week, and I always had to go with him, as he would make me feel like an unsupportive miserable cow otherwise.
Every single time, he would start playing poker, or pool or darts, and ended up ignoring me half the night, leaving me to chat to the girlfriends and wives of his mates, who I had nothing in common with. I was bored out of my skull every time, and so were the women.
When I started saying no, (after 7 or 8 months or so,) and said I am staying home, he got really arsey with me, and saying 'you'll do what you're told... and you're coming!' It ended up causing big rows, and we finished not long afterwards. Probably for the best! When I look back, I realised I should never have continued to do what he said, and not let him make me feel bad.
I know this is a bit of a different scenario, but I just wanted to say, that you shouldn't set the scene for your DH to think you should do everything he says (and wants,) and you end up doing it, because it makes him happy.......
YOU deserve to be happy too, so why do you have to do things to make HIM happy, when these things result in you being unhappy?
Upshot is, why do his wishes trump yours???