NC as fairly identifying info.
Yes it's very rude, that's undeniable. But I don't think it is fair to look through it of the lens of it just being a football match. If it is the match I assume, Sheffield Wed v Hull City then it's the biggest game this season for either of them and possibly the biggest game either will have in years. It's at Wembley for a start (I don't know the last time Sheffield Wed went to Wembley) but it's not an event that comes round all that often, possibly far less, with all due respect than a cousins wedding. And I imagine far more important to an 11 year old boy than a grown up cousins wedding.
The stakes in this game are extremely high...it's the most valuable of all the games played in the UK because of what it means for the team to reach the premiership and get the TV deals that go with that.
I don't know which team they are supporting bit it's fair to say neither team were expected to get to the final so your family are being truthful. Hull because they had been beaten twice already this season by Derby and Sheffield because they came 6th in the league and in the semis had to beat the team that came 3rd and missed out on automatic promotion by 2 goals to get there....I.e. reaching Wembley for Sheffield is the stuff of footballs wildest dreams, and for hull too after the 2nd leg.
I have family going to Wembley supporting Hull. I'm not a Hull fan but follow their progress and wish them well. Because it was important to family I went as a one off (not been since I was a child) to watch the 1st leg of Derby v Hull as an away fan (none of us live in hull but my dad is from there originally hence not going to home game). Despite not being a fan, I do occasionally watch football when DP has it on (diff team) so am not completely uninterested but I have to say being at the match (winning unexpectedly) was probably one of the best things I've done this year... it was magical. There were adults crying, men and women. I can't describe it to people who don't have an interest but what I'm saying is don't underestimate how important this is to people.
Before I get flamed, I was all set for Wembley (having enjoyed last sat more than expected) but I can't make it work (with the travelling) with plans I have on the Sunday (just lunch with friends but booked in for months because involves travelling) and I don't want to let people down.... had I been a lifelong fan, who knows, maybe I would, I don't know. I am very envious of my family who are going and not even a proper supporter. It's so important to the fans that one relative said if they didn't get tickets they were planning on going to Wembley (he lives nowhere near, is hundreds of miles away) with a sign saying he needed a ticket and was prepared to pay well over face value.
Anyway I know this doesn't help, I know you feel let down and understandly so, I'm just trying to provide some context for how they will have reached their decision because with all due respect to other posters, if you don't get football you won't understand how important this match is... comparing watching it on TV (presumably after the event if they're at the wedding) instead of going to Wembley is like telling someone to look at pictures of a beach on the internet instead of having a holiday.
I'm not for one second saying their decision is not rude or hurtful, I would be upset too, (and I reckon my own brother would prioritise such a game let alone a cousin!) I'm saying that they haven't ditched a wedding just 'for a football match's at least not in their eyes. It's nothing personal, its just that important to them.... they might not get this opportunity again for a very long time..and they aren't lying by saying they couldn't have known (it was possible but unlikely).
I do think however that if your sister is left out of pocket they should cover the cost. Please understand I'm not saying that what they have done is right, I'm just trying to be a bit more objective.... personally I would chose the wedding over the football but I can at least understand why others may not.