How often does the man use the women to enforce the abuse on the children just so he can look like the "cool dad"?

I'm just curious if anyone can relate.

All my life i was convinced that my mom was the main "culprit" because she was so overtly agressive and directly competitive with me. Her outbursts went from slapping, degradation, humiliation, etc etc. It was constant.

As a child I preferred my dad because he was mostly nice to me. But his outbursts were much more unpredictable and scary. He also had a lot of chauvinist ideas about women, openly compared my body to my mom's in front of me. Told me men will rape me and tear off my earings. Or that my husband will beat me. Or that nobody will love me because i have pimples. He glorified his friends abusive or inappropriate behaviors and I suspect he was deep into porn addiction as he often made inappropriate remarks. He was inappropriate and physically explosive at times. Never left marks (he admitted he was calculating this). My mom would just call me basic names, nothing this deep or disturbing. She did it in frustration.

When I grew up I slowly started to notice that he sows seeds of division between me and my mom. Even when my mom tried to approach me carefully (in that case she actually tried to apologize) my dad got involved and said to me behind her back that she was calling me names, a creature etc. Even if she was i started suspecting hes intentionally making things worse. Besides her approach to me was apologetic.This was one of the key rare moments my mom showed remorse and he ruined it.

Is this a common dynamic? That on the outside it seems that the woman is the main abuser of the children, but in fact the woman is "just" an overwhelmed exhausted enforcer of the man's rules? Because from listening them both speaks hes the one obsessed with control and capable of maneuvering the room. She never was. She was overworked, exhausted, unappreciated, very very angry. She looks so worn down while my dad maintained his youth. I'm starting to suspect he also abused her because I heard from her siblings that she was a cheerful giving person who'd help anyone before the marriage. How common is this?