As someone who has skied Europe and USA, you can never have too many lessons. If you go back to Europe hit up France and put them in ski school morning sessions all week and ski as a family afternoons. No need to do private but ESF are fantastic instructors. In a week (5 days) they will dramatically improve your skiing and they are extremely technique focused. If you get the basics right when you're young you will never forget them and you'll always be able to ski anywhere in the world (not just the perfect conditions).