AIO: Parent bullying/harming their own child

Since roughly two years ago, when the child had started walking, their father has increasingly caused them random physical harm. I have no doubt it’s psychologically abusive, and I’m fairly certain it would be legally considered physical abuse, but the official guidance online seems more appropriate to something much more severe, and I have had a hard time deciding which potential responses (from me) would be overreacting or potentially make things worse versus which are likely to end in the best situation for the child, both short-and long-term.

Here’s what the abuse looks like: Upon entering a room with the child, he will randomly launch a hefty throw pillow at the child’s head. Or he will push the child down, for no reason. Or while he and the child are playfully rough-housing, he will suddenly escalate and shove or otherwise use force well beyond what the child is capable of delivering in return. It’s rough enough that the child is hurt and cries, but not enough to injure. I haven’t seen him cause the child harm as punishment or with outward anger. Rather, it’s like this man thinks he has to show and frequently remind this kid that they are powerless against him. It was part of his stated approach to raising their very large scary-looking dog, and I suspect it was similar with his now-mostly-estranged son. But it also seems very much like typical bullying, with this guy needing to exert power over SOMETHING.

And the mother (whom I know better), just comforts the child each time, perhaps asserts to the child that it was not nice, maybe uncomfortably chuckles it off given the audience of other adults, but hasn’t actually stood up to him in front of me. If she’s been talking to him about it more when there’s not an audience, then whatever she’s doing isn’t working. I suspect it’s worse with an audience at this point, like he gets off with getting away with it. And I’ve hit my breaking point of being an adult who continues to allow it, waiting for the mother to do enough to put an end to it. I was so enraged after it last happened (in front of the child’s maternal grandmother and aunt, who are probably also expecting the mother to confront him), that I checked out of remaining conversation and eventually left clumsily with my own kid. I myself am an extended family member, close enough that we end up around them about every other week, and they will be at my house for Thanksgiving.

And I’m getting so angry at myself for not doing something sooner, trying to think of responses, that most coming to my mind seem like an overreaction that would only make things worse:

Threatening to document and/or call CPS would likely get me uninvited to future family gatherings, but (most importantly) would not help the child. Even if he starts behaving himself when I’m around, I have no confidence in what happens when I’m not. And I’m trying to think of a solution where he is incentivized to change (he’s mostly a reasonable person) and the mother incentivized / empowered to do her part, rather than (yet) tearing a family apart with a lengthy and traumatizing CPS process, which has other long-term implications for the child’s psychological well-being.

I’ve contemplated confronting the man by asking him why he doesn’t do the same thing with me, and then point out that the only reason he’s not is because I can defend myself, while the child can’t. While I know how I would respond if he did become physical toward me, I can’t imagine an outcome in that case that leaves the child better off.