What are some way that fathers can involve their children in family worship?

Dr. Joel Beeke explains in this video that when reading the Bible with your children, involve your children. Let your children read the passage by splitting the number of verses equally amongst the children so they each can have an opportunity to read.

Also, when your children read passages of Scripture, encourage your children to read with feeling and reverence. In short, family worship is a good time to teach your children how to read the Bible.

Psalm 19:7-9 (NKJV) - "The law of the Lord is perfect, converting the soul;
The testimony of the Lord is sure, making wise the simple;
The statutes of the Lord are right, rejoicing the heart;
The commandment of the Lord is pure, enlightening the eyes;
The fear of the Lord is clean, enduring forever;
The judgments of the Lord are true and righteous altogether."