Error is to human, so goes the old adage. However, do not turn the errors into mistakes that end up ruining your family.
Be polite or human enough to accept your mistakes, even before your children. That is how seeds of humility are sown.
In as much as you have authority over your children, it is not absolute authority. Therefore, allow them to breath, allow them flexibility that they may learn from their mistakes and become better people.
Do not allow your love for them cheat them of the chance to blossom into independent and worthy adults.