Previous post is correct. A should not have blown up. You also didn't need to point out that they should have checked their schedule first. Or possibly, it was a 'last minute' invite to the wedding ?
Just remind A that you love him/her very much, and apologize for the sillyness (if you guys even know what you're fighting about at this point). Just state that you look forward to seeing C, and it was nice of them to pay for the airfare, and you look forward to being A, Me, and C together again for a nice meal or outing. Life is too short for silly games.