I think you and others here are coming at this from the wrong angle.
it's not about you or your wife, it's about your mother.
How will she feel? Does she have a good relationship with your wife- or do they not really get on?
Your wife is being hurtful to your mum- and by inference, to you.
Has your wife made her excuses to your mum? has she apologised or suggested another family get together to make up for it?
If it were me and i had a previously arranged event which i simply could not get out of, and i cared about my MIL, i'd apologise and say offer to take her out for a meal, or invite her over for dinner some time.
Garr you must go to the party. You can't stay away simply because your wife is being thoughtless and selfish. Your duty is to your mum here.
Looking at the bigger picture though, you do need to ask if your wife is using this event as another one where she can effectively stick 2 fingers up at you and your feelings.
Without knowing all the back history to this dilemma, I'd ask- how long have both events been planned? Did either of you discuss the dilemma and what you should each do?
I think your wife is using passive-aggressive behaviour. She's either behaving in a way to test if you can be an alpha male and put your foot down, or she has given up on your marriage and is only using your home as a base whilst she does her own thing.
Which is it- and what are you going to do about it?