There's something very much off in their household, just on the start their mom didn't even want to talk to Kai, him trying to leave household in a hurry it seems and telling that Yuuto is a "hero" in his eyes... maybe he isn't that great person after all...
Don't think Kai knows about Yuuto "relationship" with Akira, but doesn't seem to mind if he would date her although he did freak out with her behaviour.
Wonder what boundaries do Yuuto will set on Akira, it's not like he does anything to her a part handheld, head pats or squeezing her cheeks...
Thanks for the scanlation!