At our gym, many parents are there throughout practice. We even have Wifi available so that we can work. There are benches, tables with chairs, picnic bench style seating. I leave work early each day to bring DD to gym, and then I continue to work once I get to gym. I'm thankful the gym has Wifi and my boss lets me do it.
We do have strict rules for parents at gym and these rules are taken very seriously. Once your DD walks through the gate and onto the floor, there is to be no communication what's so ever from that point on. If there is an issue where the coach needs your attention, you will be notified at that time.
This policy works very well, us parents police each other and strictly adhere to these rules. If we get new overly anxious parent, we talk to them and "lay down the law".
I've seen DD crotch the beam many many times, when it happens, I look, I think to myself "ouch" and go back to what I was doing. If the coach needs me, she'll come get me, but until then, I know DD is well taken care of. I've watched DD get a couple of black eyes, a head on collision, a cut over her eye, peel of the bars and land bad. Each time, I just let the coach deal with it.
Also during break time, the kids all eat together and the parents stay together, we don't interact with them at that time either. Maybe to give them their dinner, but that's it.
This has gone on for so long with so many of us, that the kids don't even realize we are there. They act and talk like we aren't even there.
If the coach needs us, we will be called, otherwise it's their show and we are just hanging out. Sometimes we leave, sometimes we stay. It's more of a social event than anything else. A bunch of us fathers talk sports all day, or the "good ole days" from when we were younger. Some parents sit on their computer playing video games for hours and hours...it's just a big hangout which happens to be a gym where they do gymnastics