The enchanted creature's controller still chooses which player or planeswalker that creature attacks.

If, during your declare attackers step, the enchanted creature is tapped or is affected by a spell or ability that says it can't attack, then it doesn't attack. If there's a cost associated with having that creature attack, its controller isn't forced to pay that cost, so it doesn't have to attack in that case either.

The controller of Skin Invasion, not the controller of the enchanted creature, returns Skin Invasion to the battlefield transformed.