For kids, I must say that a parent’s role is more important than that of the coaches. I will try to explain what they should and shouldn’t do. I am not going to name any names, but whatever I am writing is what I have observed very closely.
Sometimes kids like to play chess when it is new to them but later on they don’t like it. Here a parent’s role is to create interest with some reasonable efforts, without using any kind of force. For example you should allow them to win against you and add some stories while playing or explaining something. Once a kid is showing more interest in chess, and he is passionate about it, then it is time to introduce a chess coach and provide then necessary training.
Don’t put pressure on: It can often be seen that when two friends learn chess together, with almost equal talent, one performs better in a tournament than the other. In this case the one who is doing worse needs motivation, and at that time they are not ready to face anger or pressure as then they will lose interest in chess. And interest is key element for his or her chess improvement.
Spend time with them – if possible be with your kid while he or she is participating in any event. They simply need you as they will feel more comfortable than being alone. As your kid grows, they also need space, otherwise what is advantageous for them can create negative effects also. This can be seen more in Asian countries than Western ones.
Monitor their progress – perhaps you are the best one to judge your kid’s progress. Give feedback to his/her coaches from time to time whether it is positive or negative.
God can’t take care of every one so he created parents!