I understand you’re trying to help OP achieve a peaceful outcome but for too long women have been told to apologise for asserting themselves and for having an opinion.
You said:
”Unfortunately, the only way to get past that sometimes is to do a bit of ego massaging: ‘of course I didn’t mean to imply… you’re a wonderful father… it’s probably me, but…’”
OP should absolutely NOT be suggesting that it’s her fault or apologising for what she inferred.
He has been incredibly selfish in this instance because he wants to play basketball.
He’s suggesting he plays basketball but also watches his 3-yr-old daughter. That’s just ridiculous.
Even ignoring the safety aspect, if he’s running off the court every five minutes his team mates will be pretty pissed off. A three-year-old is unlikely to want to sit in a pushchair for long, and there’s a good chance she’ll be wriggling and trying to get out, crying, shouting, etc. And what about if she needs the toilet - how’s he going to know if he’s on court?! And then what, he’s going to take her? That’s going to be at least 10 minutes minimum off the court.
He hasn’t thought about this, and he hasn’t thought about the child.
And he certainly hasn’t thought about fellow spectators who are going to end up trying to deal with a frustrated little girl, when they only went there to watch the game!
It’s selfish in the extreme.
If there are other parents/partners there watching the game who you can ask in advance to watch the child, then absolutely fine.
But there’s no way he’s going to be able to watch his daughter AND play basketball. What happens when play is down the opposite end of the court?! He’s been selfish and thoughtless.
And then even worse, he’s being shitty to OP because she’s had the audacity to point out this is unworkable.
Sometimes things are 50/50 but in this occasion he’s been a dick. Fine if he can sort out someone to watch DD while he plays, but if not, he can’t play.
OP shouldn’t be “massaging his ego” nor insinuating that she’s wrong. He needs to understand that sometimes it’s shit but the child’s needs have to come first.