i know a 17 year old in a relationship with a 14 year old who has permission from her parents to be in such a relationship, the relationship is sexual in nature. is this permitted by law or is this trouble?

This could be trouble. Parental consent does not over-ride state law.
16 is the legal age at which a minor may consent to sexual contact.

If a 17 year old is engaged in sexual contact with a 14 year old, this is a violation of state law. If reported, there is a possibility the 17 year old could be charged as an adult.