It sounds like your staff need a slap in the face.
If they are on the roster as an operator, they are nothing more than an operator. If you are rostered as a supervisor, you are their superior. You need to stop letting people walk all over you, as you're only digging your own grave and encouraging further disobedience.
You need to be very firm and direct, but not rude. If they do not comply with your instructions, say "Either do ____ or I'll get the duty manager down here".
Try and organise a meeting with the store manager and your CSM in the one room, explain all your issues. If they are not listening to their superiors, maybe they need to be formally counseled.
There is a hierarchy of management levels that exists, and it exists for a good reason. If you're rostered as supervision, you are above them in that hierarchy.
Also, why is that guy telling you to do those "minor" things when you are supervising? Better yet, why is he telling you to do anything at all when he himself has no authority as an operator?
Also, got an operator that I hardly ever work with anymore, she stands at the service desk, and will flately REFUSE to serve customers unless they are at the smokeshop or on express, and she will not do any jobs at all.
She needs to be terminated. It's her job to serve.
Like I said. Make a list of ALL your problems, organise a closed meeting with your CSM and SM and see what they both have to say about it.