Prevent users from enabling do not disturb?

That's not possible.
If it is a discipline issue you can just look at their status (Available, DND, Invisible) in real-time in the HUD section of the app. Maybe you can then screenshot it and keep people accountable for why they did it. No need to even show them the screenshot, it's just enough for users to know sb is paying attention and is watching them.

Make it a company policy for them to always have status Available when they are at work.



Another "cruel" suggestion is to have missed call queue calls to get forwarded to 1 of the users. The user responsible for missed calls would be getting the calls even if they are on DND (because direct calls ring even if on DND) The idea here is to turn users against each other and not have everybody on the same team. I am pretty sure they would feel bad if 1 of them gets all the work, while the rest are doing nothing.