"I will give peace in their families."
What is the cause of our lack of peace? Within ourselves, and between people?
Saint Paul says it is the flesh.
In Galatians 5:20ff, he says that "enmities, contentions...wraths, quarrels, dissensions" are all works of the flesh.
The flesh is that propensity within us to seek our own limited, secondary, passing good at the expense of the higher good. It is really the principle of sin; to define what is good for me, and to sacrifice everything else, including God and other people, so that I can obtain what I say is good for me.
So Saint James (James 4:1) rightly says that the reason why we quarrel among ourselves, and therefore lack peace, is because of a war that is inside ourselves; the battle between reason and the passions. When reason does its job, it directs us to the higher good. It only makes sense that we should want what more perfectly and more permanently makes us happy. That can be none other than God.
But our reasoning powers are dull and slow to learn. Our minds know ideas, but are not seized by them, directed by them. Instead, our lower nature, our passions have a greater sway over us.
Thus Jesus says that He gives peace, but not as the world gives it. Jesus' peace is unique because only He can reconcile what is at war; our war with God, our war within ourselves and our war with others. Jesus, being fully God and fully human, reconciles all. In Jesus, God and man are at peace; in His Blessed Humanity which restored human nature to its original justice, the passions are subject to the rule of reason, resulting in inner peace. In the love of Jesus who came to forgive all, brother is reconciled with brother.
Peace, then, is a fruit of justice and order; where everyone is in his/her proper place and is given what is rightfully theirs, and gives what is rightfully expected of them. Saint Augustine said that peace is a product of the correct ordering of things.
In a world of peace, justice and order, God is God and all submit to His loving rule. Fathers are fathers in the home, ruling with love and providing for the needs of the family. Mothers are mothers, subject to their husbands who care for their wives, nurturing the children as only mothers can. Children are children, obediently taking in the education parents give so that the child can one day take his or her place in society as a contributing member in his or her unique vocation.
Our constant enemy to all this is the flesh. Pride, egotism, lack of mercy, small-mindedness, sensuality....all that points to me; all that pushes God and His rule away.
But the Sacred Heart of Jesus is a heart of human flesh, just like ours. It feels the same emotions as we feel; yet His emotions were always appropriate and in order. He had human passions just as we do; He thirsted, hungered; He even shuddered at the knowledge of the physical torment He would undergo! Let this chalice pass! Yet in this most human of fleshly hearts reigned the divine principle; God is God, and to Him we owe total obedience. Not my will, but yours be done. In the blessed humanity of Jesus, there was no inner war. All was at peace; all was in harmony. The Sacred Heart of Jesus is not a divided heart, as ours is; wanting God somewhat, but wanting our own way more.
Reflecting on all this, is it any wonder why Jesus would promise, that if someone took the Sacred Heart of Jesus as their devotion, He would give peace to their families?