Some very advanced dressage trainers do very well with children. They generally do a whole lot better than people with LESS experience who tend to get far too fussy and complicated. People get very good at explaining and breaking things down as they get more experience - it's only experience that makes a person able to see what needs to be corrected at each stage and will be the most help in making progress.
ALSO - people with experience just don't get inappropriate for the level of the student. For example, on a child's first dive into a pool, you don't sit there and lecture him for ten minutes after breaking it down in detail as if it was the Olympics. 'Good, you did it', now on to the next thing.
It is just an individual thing - as people in ANY sport that are good with children are really exceptional people.
If they have experience teaching children, or just are eager and willing to work with the child, it will be fine.
Children get very, very emotional about their sports, generally, it means an immense amount to them and they want very, very much to do well.
It isn't at all unusual for them to have tears during a lesson, even with the kindest, gentlest instructor. Children can't always understand what's happening and have a hard time putting things into words. It's frustrating to be a child and wanting badly to do really well.
And...mom...it is important to not be too protective, but to allow a child to face appropriate challenges and work it through. With stress on appropriate. So for example a nine year old can be learning to spot what diagonal she is on and change, but perhaps it will be next year before the piaffe and passage are mastered...lol.
That said I wouldn't put up with anyone who was consistently unpleasant or downgrading the kid, but if they're saying, 'Try harder, come on, you can do this!' I am not worried.