What you describe, at least as I understand it, isn't possible. If your ID is not an Apple address, i.e. @mac.com, @me.com or @icloud.com (saying it's a .com address doesn't really mean anything) you can change it to another non-Apple address but not to an Apple address. If it's not an Apple address you can't sign in with an other address. If it is you can sign in with other versions but only if you have them through being a member for a long time.
If your son has an iCloud account, and thus an @icloud.com address, he cannot move that address into your account. So I'm afraid I don't really understand what has been going on; but changing the password to something unguessable is a really good place to start.