Not that person who you replied to, but I think any discussion of who does a domestic crime more gender wise is kind of pointless, as either side can be countered by "Well there's obvious issues with reporting of it". Which are valid, because there's an insane amount of pressure on both sides to not report the issues (or perceived pressure at least), but either way, it makes bringing up a study that goes "It objectively happens more here" kind of pointless.
The second point you raise is a great example (first is pretty clear cut, I can't debate that). I think it would be hard to argue that there's not a double standard for when someone should report violence in an intimate relationships. Girls are told they should do it straight away if a guy hits them. It's much more acceptable (socially) for a girl to slap a guy than a guy to slap a girl, so I think it's valid to argue that most men don't feel like they should report cases of violence towards them.
But yeah, I don't think that abuse of children is a gendered issue at all, I've never seen anything that says one gender is worse to their children than others.