I have been sharing custody for 13 years since my daughter was 6 months old. I had a lot of the same feelings you did in the beginning.
I realized though that I didn’t want to punish my daughter for adult things either. You don’t know what she told your daughter. The best thing is to speak to your daughter about it. Truth me told, she probably doesn’t want to go to the lacrosse game. Most kids don’t always go and watch their siblings game. Find out where it really game from with your daughter. Doesn’t she really not want to go? As far as where the kid sits when she does attend the game. That she can chose. And she may not chose you, the only thing that’s going to hurt is your ego . And honestly, another day she might chose you!
My ex and I have custody of course. I have the greater amount of time. So I’m pretty flexible. If one ore t has a family thing or a birthday party, if the other parent has no plans , we let go to the fun stuff and the family stuff. Sometimes we exchange days.
It comes down the kids in the end. They shouldn’t be punished for adult decisions no matter who’s “fault “ it was. Which doesn’t mean letting them to go to whichever house they want when they want. It means considering the individual situations. But with the child first and foremost. Like if your daughter should be with her for only the duration. Of the game, not the whole day. You pick her up after, take kids for ice cream!
I am also an only child, but I did hear it is good for kids to have one on one time with each parent. So isn’t it best while you are are focusing on your sons game, for mom and daughter to have their girls time then? Or are your kids never to have one on one time or girls time or guys time because of a custody agreement?
Honestly, put your kids first, and you will likely never make the wrong decisions