Well, you typically need certain badges for traded Pokémon to listen to you.
Knuckle Badge (Brawly, Dewford Town): Makes Pokémon Level 30 and lower obey you.
Heat Badge (Flannery, Lavaridge Town): Makes Pokémon Level 50 and lower obey you.
Feather Badge (Winona, Fortree City): Makes Pokémon Level 70 and lower obey you.
Rain Badge (Wallace/Juan, Sootopolis City): Makes all Pokémon obey you.
However, that is not your problem, a legitimate Mew caught on Faraway Island by having the Old Sea Chart (which hasn't been given away at any American Nintendo promotions yet) would be at Level 30 when it is caught, and yours is lower. So, considering that Mew is basically unobtainable as of yet, and that yours it at a lower level then it should be when it is caught legitimately, all indication are that your Mew has been created with a cheating device. Nintendo put some kind of "bug" in the games that helps to identify legendaries (Mew and Deoxys) that were created with cheating devices, (this same bug also prevents these Pokémon from being able to be traded to Pokémon Colosseum) and if the absolute correct codes were not used when making these Pokémon with a cheating device, then these legendaries will always disobey you, even after you get the Rain Badge. There isn't a whole lot that you can do with your Mew. It doesn't matter how happy you make it, it will never obey you. It certainly seems like your friend has been using cheating devices, or else he is getting his Pokémon from somebody that uses cheating devices.