AITA for telling my husband his children are not my responsibility

Ok I know the title sounds bad, but read first then judge. I 41(f) am married to my husband 35(m) for 3 1/2 years now. He has 2 children from a previous marriage and we have no shared children. He absolutely hates his ex wife. Complains about her endlessly. Expects me to hate her like he does. I don’t really know her. Just what he has told me, and it’s very one sided.

They both just went through custody issues because he thinks she’s unfit. In the end, he basically lost. She had evidence of him verbally abusing the kids. I never knew this had happened. I didn’t get to see or hear whatever it was, but it must have been bad. He does have a temper. A bad one.

I don’t always agree with his way of parenting, and when I try to intervene, I get yelled at. This past weekend we had the kids and took them to his son’s soccer game. Their mother was there. His daughter went and sat with mother and he became very upset. Was complaining about it being his weekend and that mother doesn’t get to spend time with kids on his time. I understand why he’s upset, but also, it was a public event. Mother is allowed to attend these just like he is if mother brings the kids. This went on for about 20 minutes. Other parents were looking at him because he was cursing about it as well. He then asked me to go stand behind mother and daughter and find out what they are talking about and take pictures. That’s when I told him his kids were not my responsibility. He got mad and wouldn’t speak to me the rest of the game. So now I’m thinking I might be the AH because I didn’t just do what he asked.