Something tells me you received your Bastard Manager From Hell papers with a good reason ;)
As for unions, shoot to kill.
In that position your backed into a corner. If you meekly accept your authority being walked over in such a manner than you lose any authority you have, and end up being managed by the people you are nominally managing. Once that starts, it's going to be practically impossible to stop.
The only way to retain your own authority is to make it clear that if they choose to play games then you can play games back in a manner that discourages repetition.