Staff changing assignment sheets (and no respect in general.)

I am in a supervisory (supposedly) position and also do scheduling. I make daily assignment sheets as well. Certain employees take the liberty of reassigning others they don't want to work with to other halls by marking through their names. I'm getting rather frustrated about this but don't know if I should ignore it and accept it or confront the offenders. We have a DON who never seems to have a problem with anyone challenging his authority. I, on the other hand, am basically a joke when it comes to leadership--the employees basically tell me what they are going to do. I asked a CNA to get vitals on a resident in an acute situation recently and was blown off and told she had something else to do, I ended up getting the vitals myself.

It's like, who's working for who?

I do have a temper but showing me gets nowhere. Write ups get thrown in the garbage (if I write them). The facility likes having me around, I'm helpful, run errands and labwork, do this and that, clean and organize the DON's office...but when it comes to respect I feel like I get none and it's really getting me down. The pay and hours are good and I know leaving would not be smart, as so many other factors come into play when it comes to reasons to keep this job. Just looking for insight, words of wisdom, suggestions...