Would you ask users to change or do you change your development process?

As a internal IT team, our challenge is to have a clean process of request, changes, test and release. However, we have people just coming directly to developers and they want things done immediately. That's good for the users but it just creates a mess. We have hard time tracking who did what and often get ourselves into this loop of fixing things. Once fix breaks another and we are in this cycle since a while and doesn't look like it'll end.

So, would you tell users to work in a different way to fix the development process ? Or would you continue or change current way of development?