Was it wrong to arrive late to my daughter's engagement party because of my son's sports game?
Why did you stay at your son's game when you had to be at the party?
I didn't have a choice, my son is the captain of his team.
Your son has lots of games, but your daughter only gets married once. Showing up late likely hurt your daughter a lot more that had you left your son's game early. Sometimes we have to prioritize events by how important they are to our loved ones in the long run.
I'm serious my son is a basketball prodigy.
I understand that you are passionate about your son's basketball career, but you should have been there for your daughter. It would mean a lot to her if she had her dad by her side on the day of her marriage. Make the sacrifice and miss one game next time to see your daughter instead.