Working within Union guidelines as a supervisor can be tough. I've done it and what helped me tremendously is learning the rules by heart, and great documentation. I've taken over divisions with lazy slugs with the outgoing personnel telling me "It's impossible to fire anyone with the union". That translates into "I'm too lazy to document their performance and conduct in order to successfully change their behavior or terminate them, so good luck with my mess"
If they work for you, then if anyone has to be miserable at work, and the choice is you or that slug.. it should be that slug. Good paying jobs aren't that easy to find these days, hard working people who need a good job who can replace your slugs is a lot easier to find.
just my .02