I've heard that broken bones heal stronger than they were prior to the injury. I haven't confirmed this as medically true, but I believe the same is true for broken relationships.
When I apologize to my children, it causes them to trust me more.
When I let my children know that my attitude with the cashier at the store was wrong, it causes them to respect me more.
When I ask my husband's forgiveness in front of my children, it causes them to love me more.
Humility draws others closer to us. Pride and unwillingness to ask forgiveness pushes people away.