I can very easily believe that the brother forgot the date of his brother's wedding. I was bridesmaid for my sister less than 6 months ago and if you asked me to tell you the date it took place I'd have to stop and think about it, and I am generally good with dates. The event and the individuals concerned were, and are, very important to me, but the specific date? Not so much.
Also, it sounds as though neither LW nor her husband have actually said anything to Brother about the clash, so they don't know whether or not he remembered, or whether he and his bride would be able to move the engagement party.
I think they'd be fine to decline attending the party and to explain that this was because they already had plans for celebrating their own 1st anniversary that day. But I also think that for something as important as a sibling's wedding (and apparently the brothers are close enough that H asked his brother to be best man), LW and her husband should be prepared to go to the wedding even if that means that celebrating their **2nd** anniversary takes a back seat.