We have to discipline our children and teach them that disobedience is a very serious thing—disobeying parents, disobeying God. We must teach them to be honest. We must teach them to be faithful in small things. We must show them the examples in Scripture, how so many Christians have suffered for the faith for standing up for what is true. That is how we prove that what we believe is right.
You can read them stories of the martyrs. There are many books about Christian martyrs through the years. Read them and tell them those stories. That'll encourage them to be faithful when the time comes for them.