Perhaps because he feels that he has no other choice. What if he was coerced into this relationship with the mother? A typical rich exploits the poor or drives them into believing they've got no better option type of situation. Maybe he had an entirely different personal reason but was still coerced under the illusion of free choice. At least that's what the flashbacks during his drugged scene hint towards and also his words to Rosa (whom he thought to be her mother at the time).
If he doesn't go along with what the mother wants (for the two to get along) he's afraid of risking the benefit he reaps from this relationship or whatever effort/sacrifices he's made to reach this point. And all the while maybe he wants to convince himself he is living a normal life (one devoid of the hardship that comes with poverty or being orphaned — althought I don't really know if he's poor, or don't remember. He doesn't strike me as the guy to go into sex work for the love of the game).
Thats your assumption or one sided perception.. as far as the story progressed it seems like he doesn't necessarily have to get close to rosa to get along with her.. he has this tendency of acting close to others or try to be on everyone's good side just like he did with the gardener lady.. but he didn't necessarily need to do that either.. even if the mother and his relationship is forced, he doesn't have to constantly turn up everywhere rosa goes.. he's not even forced to get along because the mother hardly cares about him.. its just him who's repeatedly getting on someone's nerve who doesn't like him and see him as a family.. him acting like everything is fine and playing "happy family" is downright ridiculous... And rosa being the stubborn egoistic person she is, she's trying to make him uncomfortable and understand the harder way that what he's thinking is stupid..she even mentioned a few times that she doesn't need a dad or a family...it so vividly clear how she is taking the whole thing...so i don't understand why he's trying to force a happy family relationship with her....
so none of the reasons you gave have anything to do with getting close to rosa, thats just him, trying to act nice guy when even he knows how nonsensical the whole "happy family" set up is.
I don't feel sorry for the guy at all.. he keeps crossing the line trying to act all friendly with rosa, someone who obviously doesn't like him .. why is he trying so hard to get along.. its embarrassing enough to call someone that young your "dad".. he should stay away from the girl but no... Rosa is trying to prove a point that its not possible to act as a family because she doesn't see him as one...