Hyper-grace preachers who assert that grace has done away with the need for the law should read carefully Paul's use of the Ten Commandments ("Honor your father and mother") to back up his admonition to children to obey their parents. If the Law is irrelevant under grace, then Paul is contradicting himself. But Paul never denies the role of moral obligations of the law, only the religious aspects, especially the rites and rituals under Judaism. But the Law is still relevant to NT believers as a guide to godliness, though Paul rightly teaches that the Law cannot save us from our sin--only Christ can. The purpose of grace is to empower us to obey the spiritual and moral obligations of the Law, not to make them irrelevant.
So, Paul sees no contradiction between Grace and the Law, but only that we are not to rely on the works of the Law for our salvation but to rely on Christ's completed works on the Cross. Anyone who teaches otherwise is deliberately selective in his reading the Scripture and even deceptive by ignoring Paul's writing that does not fit his theology of grace.
In this passage, Paul is writing to the church at Ephesus about the importance of proper submission to and the proper exercise of authority. Children are to obey their parents because the Law commands it: "Honor you father and mother that it may go well with you and that you may live long in the land" (Exodus 20:12; Deut. 5:16). But fathers are not to abuse their authority but to use it to bring their children up "in the discipline (deeds) and the instruction (words) of the Lord." The word "discipline" (paideia) has been translated elsewhere as "chastisement" or physical discipline while the word "instruction" (nouthesia) refers to admonition by words. So good and godly parenting involves physical discipline and verbal admonition. Parents who subscribe to the idea of disicpline as "abuse" is disobedient to God's Word and will reap what they sow later in life when their children turn wayward.
Similarly, in the workplace relationships, "slaves" (employees) are to obey their earthly "masters" (bosses) with "fear and trembling". So, submission of employees to employers are expected in the workplace. But again, bosses must not abuse their authority by threatening them with pay cut or dismissal because God is holding us accountable regarding how we exercise our authority.
While the exercise of authority implies the response of submission (obedience), we as Christians must be careful not to use that as an excuse to "lord" over those under the authority. God grants parents and bosses authority in order that they may use it to serve those under our authority, viz., to promote the spiritual and moral welfare of our children and our employees. Carnal authority is self-serving but spiritual authority is other-serving.
Father, You have shown us how to exercise authority to serve those who obey You. Teach us to use our authority to bless rather than to burden our children or employees. Amen.