I want to defeat the Battle Maison with a friend over online, but I can not find a way to do it. Is there a way I can do it over Wi-Fi/Internet (My friend said you can only do it through local, but he is not 100% sure).
As far as I can determine, this is not a thing that is possible. In order to set up a multiplayer Battle Maison, the game requires that you and your partner establish a infrared connection.
Presumably this is to ensure both persons are in the same room and can communicate, because the infrared connection is only used for the initial setup. As after the setup, the 3DS units are no longer required to be pointing at each other.