I Timothy 1:13-14
Who was before a blasphemer, and a persecutor, and injurious: but I obtained mercy, because I did it ignorantly in unbelief. And the grace of our Lord was exceeding abundant with faith and love which is in Christ Jesus.
All of us are born sinners. Our struggle comes after we are saved and realize that we still fail daily to live up to the standard of Christ's perfection. There are times we sin in ignorance, copying what we see around us or what we have always done and there are times when we sin purposely because we want what we want.
As Christian parents, we know our children need discipline. We have all read Proverbs and know the need to train up a child and not to let a child go his or her own way. But I think sometimes we miss the spirit of this verse. God is our Father, and while sometimes, He corrects us because of His love for us (Proverbs 3:12), sometimes He also shows us mercy.
There are sins of ignorance, those committed without malice and without knowledge that what we are doing is sin. In those situations, we need to show mercy and grace to our children, with love. That will probably mean not disciplining them but that doesn't mean there will be no wisdom shared. What was one time done in ignorance, can not be done in ignorance twice. They must be told what they did was wrong and that there is, with the knowledge of wrong, a responsibility to "go and sin no more". Grace is not license to do something again and it is very important to show both grace for ignorance and correction for willful continuing in the sin.
Of course, there are times to continue to show grace, God gives us plenty of examples of times when He shows mercy and grace when we are quite aware of the discipline we deserve. But we must be sure, we are showing mercy and grace with love, not ignoring the problem because it is inconvenient for us to deal with at the moment or "not a big deal" or some other excuse not to show that we love our children enough to take the time to correct them. Children need to know they are loved. Sometimes that means a hug and an "I forgive you". And sometimes it is a correction that may mean they are unhappy with us for a while. But either way, it must be love that motivates us, just as it is love that motivates God.