Personnel issues cannot be solved with technology, as I'm sure you know. There is no built-in capability of Exchange that allows for some kind of captive waystation where outbound emails are approved or denied. Certainly you can use transport rules that forward emails from certain mailboxes to other mailboxes. You can keep tabs on things that way. However Exchange is a UC platform, not a personnel workflow management system. You'll need third party tools to allow this to happen.
Yes, Exchange has a rich API and developer platform, so I'm sure you could figure something out. However, guidance on developing a tool like this is, in my opinion, beyond the scope of ServerFault. You will need to fundamentally alter the way that Exchange manages the flow of email.
Your best bet is to look for a pre-built tool that allows for this kind of management. However, before you ask "What tool would do this?" you should know that ServerFault frowns on product recommendations and will likely close that question.