Kaoruko was afraid of inconveniencing Rintaro because he might not be ready to face her family just yet, but our good boy exuded a confidence that he can handle it, with her permission of course. (He's mostly winging the confidence part, but the fact that he didn't just run away and say no or make an excuse to do it next time is already a win in itself, he has guts merely saying ok)
"If your family knows we're going out, I want to greet them properly."
Wild looks aside, he is in fact among the better guys a parent can hope for their daughter. He has manners, is considerate and respectful.
Maybe little bro Kousuke is just making up for the fact that he snacked on half of Kaoruko's birthday cake that Rintaro specially baked. He's giving them a good push, maybe too good (so maybe someday he'd have a cool brother-in-law who'd bake him a cake too).
"Thank you for falling in love... with our Kaoruko."
Such trusting words from her mother. Can I take that as her approval?