Apologies if another poster has mentioned it but perhaps we have all forgotten that it is not just the groom (the brother in this case) that has planned the wedding and engagement party on that date but also (and maybe even likely more so) his fiancÚ. She has also picked that date. LW even says that her and her husband barely know the fiancÚ. Therefore the date LW and husband got married will have even less significance to her brothers bride-to be than her brother. As they barely know her, maybe she didn't even attend their wedding in the first place or if she did, I doubt the date would have stuck in her mind. There might be 1001 reasons the couple as a couple (or maybe even just the bride!) picked this particular date for their wedding and engagement. At least 50% (assume for simplicity) of the decision making for the date will have come from the bride and the date might have been picked for reasons on the brides side that we have no clue about. There are two lots of family considerations and guest conflicts to consider. Even if the brother did remember, it might not (understandably)be important enough to his bride to pick a different date. She barely knows these people and they are not close to her.
I'm with the people that do not understand why a certain even has to be celebrated on a specific exact date. Surely it is about the sentiment, the gesture, the milestone rather than the specific date or exact time itself? I actually doubt the majority of adults and children celebrate their birthdays, valentines day, anniversaries with a "celebratory event" on the exact day as there are more weekdays than weekend days. I think most people celebrate to the nearest Friday or Saturday night either side. In fact, you can "celebrate" actual day itself by perhaps exchanging presents then and having an extra passionate kiss, but leave the "celebration event" e.g. dinner and dancing, for the day before or after. If anything, it prolongs the romance!
Whatever the LW feels, she should be sincere and polite with her BIL. If they really really want to celebrate their first anniversary on that exact date and decide that it would not be as special celebrating it the day before or after then they should politely decline the engagement party. If I was the LW I would be sincere with my BIL and tell him that I was very sorry I had to decline but that the first anniversary date was very significant to me. If I was the BIL, I'd rather have this than a guest show up reluctantly who wouldn't enjoy the night or celebrate fully because they clearly preferred to be somewhere else.
However with regards to the Second Anniversary vs The Wedding, it would be extremely hurtful, immature, churlish, consequential etc.. etc.. not to attend. I think they would also end up regretting it down the line. I don't think there's anything wrong with celebrating a second anniversary if it's important to them, but to celebrate in lieu of BILs wedding would be a very bad idea.