He can't own Disney stores. Only Disney owns Disney stores. And even the remaining Disneys themselves don't actually own Disney stores.
But your first part could totally work: His dad can work for Disney and probably be like a head manager that oversees Downtown Disney. I honestly have no idea what that title would be, but it would be more believable.
However, and maybe the mods would think differently, but none of that would have to go in the local directory since it's already all covered under Downtown Disney.