You could help your children appreciate this feast by talking about how it feels to have good news to share, and how it feels to get to hear someone else's good news, too. Maybe you could take a couple minutes to listen to each other share a piece of good news-- especially what you are thankful to God for today.
The other part of the story is that while both women were experiencing miraculous pregnancies (Mary as a virgin, Elizabeth as a woman long past child-bearing years), they both surely had concerns and worries connected to these great gifts. They supported and encouraged each other-- something that (hopefully) comes natural to family. Are there concerns and worries that your child and you can help each other with, and can pray for each other about?
As we come to the end of May, the month dedicated to Mary, praying the Hail Mary together would be a lovely way to conclude your family conversation.
Hail Mary, full of grace,
the Lord is with you.
Blessed are you among women,
and blessed is the fruit of your womb.
Holy Mary, Mother of God,
pray for us sinners,
now and at the hour of our death. Amen.