is it normal to have lessons/compete without any kind of helmet for children? Noone seems to (including teacher) and DD insists it will get in the way. However I am concerned about her cantering around bare headed.
Yes, it is. At higher levels they would really get in the way. Riding for the Disabled vaulters wear them, but not other vaulters. If you are not happy with it then you may have to stop her doing the activity. it has to be your choice balancing up the risks.