Please explain what a parent can do sitting in our living rooms, other than back up any disciplinary action a coach might take, or pulling our kids altogether.
I know how I want my kid to behave, and I know how I would firmly correct her behavior if I were there. And trust me, I'd be effective. But I can't effectively discipline my kid from miles away. I'm counting on you to do that. And then I'll back you up.
It's not about disciplining the child from miles away, or sitting in the gym waiting to step in if your child acts up. But laying out expectations for your child before hand. Letting them know they are to be respectful of their coach, and exactly how that should look (looking at coach when he/she is speaking, following directions, working to the best of their ability) as well as what the consequences are for when the coach reports back to the parent that their where problems in the gym. Also, keeping an open line of communication with the coach if you know your child is prone to certain behaviors in the gym and give them ideas on how to deal with those behaviors (sitting out is a great solution for some kids, for others it just exacerbates the problem).
As for the OP's gymnasts, I have some groups who have gone through spells of similar struggles. If it is a safety issue, I tell them they need to get down or sit out until they are ready to focus on what they are doing because I am not willing to see them get hurt. If they pop up for their next turn I let them give it a go, and if they continue to be sloppy or lacking focus, I tell them to get down and repeat myself. At least for my kids, this usually works.
For some kids, if the behavior is not safety related, I will sometimes just let them go and ignore it. When they realize they aren't getting attention for acting out, they get back to what everyone else is doing and I start working with them again.
I also try to give lots of praise to kids who are following directions, listening, working their hardest so the others can see that you get attention by being hard working and respectful.
I also try to remove distractions as much as possible. While this is impossible for distractions like rec. classes, it can be done with mats the kids like to play on (for us the round bhs mats are a HUGE distraction) or other odds and ends that can be found around the gym. Though this is more a problem with my 5-7 year olds than my 8-12 year olds. And like gymdog, I have more overly active kids who race through everything and jump around during instructions than kids with lie around or take extended breaks.
For my pre-team kids (ages 7-12), I have on occasion sat them down and talked with them about behavior expectations and consequences for not behaving appropriately.
All kids are different, and sometimes it takes different steps to get all kids to respond. But I've found that once you get the majority of kids on board, the remaining few will either shape up or see themselves out.