Is it permissible for a young child to see the 'awrah of his parents, and is it permissible for him to bathe with them?

It is not permissible to expose one's awrah (private parts) in front of discerning children, for Allah Almighty commanded the believers to instruct those who have not reached puberty to seek permission at three times. These are times when people may shed some of their clothes, so that children do not see the awrah and grow up accustomed to covering it. As for a non-discerning child who cannot recount what he sees, there is no harm in not covering from him.