In the declaration of independence, the colonists complained that the king had taken control of the judges in their court system. which enlightenment idea was most violated by this action by the king?

This violated the separation of powers idea

The separation of powers was that power should be separated between various people or institutions in order to ensure that the government is fair. If the King controls the courts then the courts just act according to the King's will, even if the King does something that is illegal which means that the King is a tyrant and an absolutist.