Jamais, your comments about his public persona which is entirely at odds with his private persona reminded me of my grandfather, my DM's father. He and my granny were GPs in a small rural community and I always knew that my grandfather was admired and respected by his patients. I also knew that my grandparents' marriage had always been an unhappy one. My DM once said to me that she "didn't think" he hit my granny, which means that he might have done. He certainly had affairs, and kept her short of money. I knew him as a man who was domineering, refused to let my granny socialise with her friends. As an elderly woman, my granny had a miserable life with him. They have both been dead for about 20 years now.
Anyway, a couple of years ago, my work brought me into contact with an elderly couple from the village where my g/parents were doctors. I did a home visit with this couple and in conversation the woman worked out that I was The Doctor's grand-daughter. She was beside herself with delight and told me how wonderful my grandfather was, how he had visited them in that house, had sat in the very chair I was sitting in! She waxed lyrical about how wonderful he was, how handsome, how clever, how attentive a doctor and on and on. Full on hero worship. And I sat there and smiled and nodded.
And I left their house, drove away and had to park up before I went back to work, and had to take time to process the massive disconnect between this Hero, and the man I knew. The experience really unsettled me, and then I thought - that is what my mother grew up with! I'm a generation removed, and it was just one conversation, but my mother and her sister and brothers had to live with this misplaced hero worship of their, behind closed doors, abusive father every day!
As it happens, one of my neighbours is ages with my DM, grew up next door to her and is still friendly with her younger brother. That neighbour said to me last year that my mother and her siblings were always callous. That there was a hardness about them. (This wasn't just a random remark - it was relevant to the conversation we were having at the time) I can see that that hardness, that callousness, came out of living with the disconnect between their father's public and private personas, particularly growing up in a small community where he was well known.
Your children, like my mother and her siblings, will also come to know, if they don't already, that disconnect, and it will affect them in some way.
You know, he won't change. He might be able to put on an act to appease you for a while, to keep up appearances, but he is who he is.