"Children, obey your parents in the Lord: for this is right." (Ephesians 6: 1)
The better translation of the word "right" is "righteous."
Now, we are not righteous because of our actions.
We are righteous because of what Jesus did at the Cross for us:
"15But not as the offence, so also is the free gift. For if through the offence of one many be dead, much more the grace of God, and the gift by grace, which is by one man, Jesus Christ, hath abounded unto many. 16And not as it was by one that sinned, so is the gift: for the judgment was by one to condemnation, but the free gift is of many offences unto justification. 17For if by one man's offence death reigned by one; much more they which receive abundance of grace and of the gift of righteousness shall reign in life by one, Jesus Christ." (Romans 5: 15-17)
"20Now then we are ambassadors for Christ, as though God did beseech you by us: we pray you in Christ's stead, be ye reconciled to God. 21For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him." (2 Corinthians 5: 20-21)
Righteousness is a gift which we have received because of the blood of Jesus.
So, what does Paul mean when he writes that children should obey their parents because "it is righteous"?
He speaks to the fact that obedience to our parents, just as men and women submit to each other in the Body of Christ, and wives submit themselves to their husbands, is a response to God's Son submitting to His Father and granting us His status at the right Hand of the Father.
We obey our parents because we are righteous, and that is what righteous people do.
The world still does not understand the grace and glory which falls upon us from submission. Consider the specific example of David with his father Jesse:
"And Jesse said unto David his son, Take now for thy brethren an ephah of this parched corn, and these ten loaves, and run to the camp to thy brethren; 18And carry these ten cheeses unto the captain of their thousand, and look how thy brethren fare, and take their pledge. " (1 Samuel 17:17-18)
While David's elder brothers shamed him for trying to promote himself, the truth is that he was obeying his father, and this obedience placed him in the position for God to promote him before King Saul:
"So David prevailed over the Philistine with a sling and with a stone, and smote the Philistine, and slew him; but there was no sword in the hand of David." (1 Samuel 17: 50)
"56And the king said, Inquire thou whose son the stripling is. 57And as David returned from the slaughter of the Philistine, Abner took him, and brought him before Saul with the head of the Philistine in his hand. 58And Saul said to him, Whose son art thou, thou young man? And David answered, I am the son of thy servant Jesse the Bethlehemite." (1 Samuel 17:56-57)
While David could have been sullen and disrespectful (after all, he had been anointed king long ago), he obeyed his father, and God was able to bless him with greater favor and honor.
Today, children can know that when they obey their parents (when they are not contravening His Word), they are due to receive the blessings of grace which fall on them, because they are righteous by faith in Christ.