There are laws that apply to members of the executive branch, even though that branch is also responsible for enforcing the law. So how to handle the fact that that means they can break them with impunity?

The answer is that the Constitution give Congress abilities like impeachment specifically to give them the ability to apply pressure and "enforce" that the executive branch does what it is entrusted to do.

The exact same situation applies to police. Surely you understand that it is possible for police officers to break the law even though they are technically also the people responsible for enforcing it?