I am hoping that the BvS Ultimate Edition fixes many of the issues with the original cut, though nothing is gonna fixI think you not caring about the character's motivations was less about them not making sense and more about you not caring about Bucky. Cap was dead-set on proving Bucky's innocence because Bucky is literally the last living connection to his past life. He also swore to never give up on Bucky and has known him longer than he's known any of the Avengers.
Tony's been having an obsession with making the world safe from his monsters since Iron Man 1, going so far as to build a new monster to protect the world from space monsters, which backfired immediately. That deep-seated fear combined with the collateral damage caused by the Avengers is pretty much his driving force behind taking the political side that he does. He also feels betrayed by Cap because despite their constant butting heads, he considered him a close friend, and Cap's choosing Bucky over him, which makes sense considering his past history with both characters. The rest of the characters just pick sides based off of what they thought was right.
And even though the ending was somewhat weak, at least they didn't walk it back immediately like BvS did. BvS does have good moments (Batfleck is awesome) but it is still incredibly flawed.
"MARTHA".