I've been thinking about this. There are so many things, and I can't remember any of them lol
1. To go off what @ct_dad
said, be the parent ALL the time. Support them, and be their cheerleader. But most importantly, don't let them hear you if you decide to talk about the coach. Kids feed off your energy. There have been numerous situations when I've heard kids tell coaches that their mom/dad said this, so now I'm going to say this too. It just creates a terrible atmosphere.
2. Everyone wants to win. However, I have always been a big believer in losing teaching more than winning ever will. Learning how to lose with grace and win with dignity is a tough lesson. Made worse when the talk of "this team cheated", "we were robbed", "they paid off the judges", or "they just don't like us" etc is all that's heard. Help the coaches teach your kids that sometimes, the other team just had it that day. If it's your coaches saying those things, maybe find a new gym.
3. Any coach worth their salt is not going to care who is doing the job, as long as the best person for the job is doing it. Don't (seriously) get hung up on position in routine. So many people get caught in the "my kid has always flown, and that's all she wants to do" black hole. There's no coming out of that. The best person for the job will get the job. Seniority means absolutely nothing when it comes to being competitive. In addition, the stress and pressure this places on the child is enormous. If they aren't in the air, or last pass, or center dancer that doesn't mean their position on the team is worth any less.
4. Don't let your kid be a gym rat. The vast majority of those kids burn out and quit. They should have other interests, other friends, other things going on. It's great when they're 12, they can't get enough of it. Then 14 hits and they're tired. They need to spend a healthy amount of time in the gym. Practice, team tumble, 1 private/week, maybe 1 open gym. Eventually it'll catch up to them. Not to mention the wear and tear on their bodies. Make them take a break.
5. Enjoy every single moment. There is a very short window of time when your kid is going to want to spend their time with you. Enjoy every single memory made on those weekends spent in a terrible convention center with even worse food. Don't worry about all the little things. You won't remember them when you look back. You're going to remember trying to figure out how to do your kid's hair and makeup. You'll remember having to get the pixie stix or dippin dots cause "tradition". You'll remember those inside jokes you have with other parents, that no one would ever understand or find funny unless they were there. You'll remember your kid coming to find you after a performance, good or bad, to find out how they did. The tears, the cheers, and everything in between. Enjoy it. It's over before you know it.