When I saw your initial title, I assumed: a) he was older and joking about looking like your dad; b) it was a cultural thing, like some Latina women calling their partners "papi"; or c) he was just struggling to switch from "mum and dad" mode back to adult mode.
But having read your posts, it’s clear he’s a belittling, boundary-trampling knob-womble.
Even if he's not using this language in the bedroom, it’s clearly a power play with sleazy undertones. As disturbing as the language is, I’m more concerned by how he gaslights you, dismisses your feelings, and weaponises your ADHD to put you down.
If I’ve got this right, he’s been told to stop but keeps ignoring you. This seems to give him a thrill—imposing his will and language on you. His "spontaneous" hugs and kisses are less affectionate and more about scaring or unsettling you, and his so-called "banter" about wives being property is just toxic.
The fact you have sons makes me think he’s using "daddy" to assert himself as the primary figure in your life, grinding you down to feel dependent on him.
Please, consider making plans to leave. This isn’t just a "weird habit"; it’s a cluster of coercive, demeaning behaviours that scream “danger Will Robinson.” Set yourself and your boys free from this bullshit.
And yes, the chances are high that this language ties to a sexual kink and porn habits —"daddy" and "praise" kinks come to mind. I’m all for "you do you," but not when it’s imposed on unwilling people.
I strongly suspect that this type of porn has buttered his parsnip precisely because of the dominance and power subtext. The issue isn’t kink itself but that he’s a nasty controlling shit gibbon WITH that proclivity.
As someone with ADHD who’s left a toxic relationship, I say: you can do this. A happier life for you and your boys is possible without him.