August is a tough nut to crack and I don't think we should get too far ahead of the evidence when discussing his love for Hana. He feels something for her, but there are many kinds of love. August wants a better relationship with Hana, but it's not clear why he wants that, nor is it clear what he would or would not be willing to do to earn that acceptance.
On the why side, his motivation makes a huge difference - even if we assume he isn't malicious. Going to see Hana's concert in secret, for example, plays very differently if you think he wants to learn her tastes to better convince her to see reason (from his point of view) versus if you think he wants to see her while she's happy without embarrassing/offending her. Likewise reflecting if he was right to involve Hana in the Club could be a fear that he's leading her down his own path to damnation, or it could be a concern that she isn't up to task of being a criminal boss. Either way he cares for her, but in some cases that care is as much about him as it is about Hana herself. My gut reaction is that August is being at least partially selfless in his love for Hana, but that may just be wishful thinking.
Similarly, we don't really have a good read on how much August would sacrifice to change Hana's opinion of him. We know he's willing to use Hana's dying mother as leverage and that he'll happily throw money at the problem, but neither of those really cost him much. What if it became clear that shutting down the Carnation Club and living a meager life as an honest man would cause Hana to change her views on him: would he do it? Does he want his daughter to accept him as he is, or would he change his ways if that would make him someone she can admire? Until such a situation comes up all we can do is speculate.
Personally, I don't think August would alter his core tenets for Hana because I think he wants a certain level of validation from her; even if she doesn't approve of his actions, he wants her to accept his reasons for taking them. Of course, one of his core tenets seems to be pragmatism, so I do think he'd be willing to alter any of his lesser tenets if that would do the trick, and he doesn't necessarily have to keep making the same decisions going forward.
That would require that Hana agree to spend *any* time with August, and she flat out refused that when he first offered.
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August used Hana's mom as leverage so he could get his foot in the door, so to speak. He probably figured it was the only way he'd have a shot at changing her mind, and since Hana already hated him there was nowhere to go but up. Obviously he could have simply continued to help her mom without strings and hope that would eventually bring Hana around, but for whatever reason he was unwilling to take that chance.
Again, I think it all comes back to why August wants to spend time with Hana.