This is so weird but it reminds me of my own dysfunctional family. The language is dramatic and not right, the behavior on all sides is messed up too ; begging, restraining, holding round waist, wtf. No.
If your family network is dysfunctional then you don't realise sometimes what's actually going on.
People would now accuse me of acting like I have a rancid UTI. The truth is, I've finally woken up to how fucked up it is and have detached significantly from it. I now speak my truth too. So I appear like a different person. I'm simply growing through the fucked upness and dint want part of it any more.
I can't really tell who plays what role in this dysfunction you describe. Your dad's dramatics are like a child. It's possible that this is a build up of so much you don't realise and he's flipped because of multiple frustrations.
I have a dynamic where my own teen will be a twat to me, egged on by highly narcissistic family members. Not ok with me anymore. After years of it, I've cut off from the main perpetrator (a male sibling). Be very careful what your teenage son is observing. I don't care if he's a typical teenager, he needs correcting and to be respectful. So good to keep letting him know you are to be respected as the key person of importance; his mother.
What you said to your dad - I'd be very pissed off by that comment. But, is your dad usually a dick? Is he usually used to having full power and control and that comment you made shows that's gone now, so he flipped? Sounds like your mum panders to him? Is he a long term dick who expects to be treated preferentially, who demeans the women? Or is more going on and he's just had enough? I can't entirely tell.
Hindsight is great - if it was your correcting the teenager that he was commenting on, I would say ' please leave me to parent thank you'. I don't see that as disrespectful. It also makes things very very clear to him, to your teen and anyone else listening. I sense that you get disrespected and belittled at times.
I feel you need to back away, breathe, stop getting so desperate about this. It's feels infantile ( I understand as am in a fucked dynamic). Leave him be and stop feeding this silly drama. The more desperate you act, the more you encourage unproductive dramatic behaviour. Things should not be swept under the rug either. My entire life has been built on a family that sweeps every weird inappropriate thing under rugs.
If he has something like dementia then only time will tell. Treat him as if he doesn't and it's actually explainable until anything changes to suggest he is ill.