When sending my kids off to be with others it is always my prayer that we have trained them well enough that they will be a blessing - not a headache for others to be around. In various kids lately I have had the opportunity to observe both the absence of training and the result of training. The results are SO different!
Anyway I think it is extremely important part of being a parent and here are some verses that express that importance as well:
"Train up a child in the way he should go; even when he is old he will not depart from it." Proverbs 22:6
"Discipline your son, and he will give you rest; he will give delight to your heart." Proverbs 29:17
"Fathers, do not provoke your children to anger, but bring them up in the discipline and instruction of the Lord." Ephesians 6:4
"Children, obey your parents in everything, for this pleases the Lord." Colossians 3:20 (If this is going to happen, we are going to have to make it happen.)
"Whoever spares the rod hates his son, but he who loves him is diligent to discipline him." Proverbs 13:24
"And these words that I command you today shall be on your heart. You shall teach them diligently to your children, and shall talk of them when you sit in your house, and when you walk by the way, and when you lie down, and when you rise." Deuteronomy 6:6-7
"Discipline your son, for there is hope; do not set your heart on putting him to death." Proverbs 19:18
"Children, obey your parents in the Lord, for this is right. “Honor your father and mother” (this is the first commandment with a promise), “that it may go well with you and that you may live long in the land.” Ephesians 6:1-3
Another great resource in encouraging you as you raise your children is this video called "A Peaceful Home" by Elisabeth Elliot. It is long but I think you will find it very encouraging and helpful. There is also a part 2 which is very good and you can find on Youtube.
May you always seek God's wisdom as you train your children.