I'm not seeing the comparison between Q2 and Q though. Q2 was tasked with stripping Q of his powers because the Q Continuum/Q2 got tired of constantly apologizing on behalf of Qs bullshit, the same thing that Trelanes parents had to do. He didn't like humanity but I mean none of the Q in general seem to "like" them so much as tolerate as you mentioned. Some Q fuck with humanity but only now after Our Q has fucked with humanity. They seemed to have exactly zero interest in us until randomly during the Encounter at Farpoint one particular Q gets pissed for seemingly no real reason and starts toying with them like an asshole, Trelanes bit almost to the letter. Even going so far as to throw Humanities history in the face of them now while only understanding the form and not the substance (same as the food and fire).

It's just bizarre to me that no one in the Q Continuum gives a fuck about humanity at all for millenia, then a child messes with them for a short period of time, everyone ignores them again and then randomly there's an adult Q whos hellbent on fucking with Humanity at every opportunity.