
Don't know if this helps.
1) Akitora has wife, sleeps with Rogi - Akitora is a Yakuza. They run their businesses, they kill and they fuck. Normal morals and ethics don't apply to them and being a wife of one needs to adjust to all of that. It's not a problem, really.
2) Why Rogi? Theory time: Akitora admires, is attracted to, is jealous of Rogi's YOLO life. He gets to do what he wants for himself. He has twisted morals and that's okay. Rogi is "free". Akitora's the same, free-spirited, but he can't truly be one because he's bound by rules that he also reveres to at the same time. He sees himself in Rogi. Or Akitora just wants to

Again just a theory, I think Akitora loves her. I assume he's someone who wouldn't do such a half ass thing to marry someone solely for Yakuza purposes. I am getting confused whether Asami was a former prostitute or she came from a Yakuza family and they were childhood friends. If it was the former, I'd like not to think their marriage started off from pity (though highly doubtful that). If it was the latter, reasons to marry: Yakuza duties >> love. Ugh, I need to reread. But I am pretty sure Aki loves his family and plays around at the same.
Ok I'm getting confused about the relationships here,can someone clear this up for me? So Akitora has a wife but he slept with Rogi? Why? I'm so lost