Family prayer, in its highest form, involves the whole family. Does God only speak to adults? Do children, even young ones, not need to bring adoration and supplication to their Heavenly Father? We must be careful to include even the youngest of our clan to talk to the Lord, and to hear from Him.
Let everyone express the Lord in their own ways. (1 Cor. 12:4-12) We all have unique ideas and vocabulary (especially children!) and prayer is not the time to be restrictive. Be careful correcting grammar or topics of prayer. When I pray with my children I take care that they are praying according to Scriptural guidelines, but aside from that I let them talk. I would not police their conversations with friends or grandparents, so why would I with God? Maybe they would rather draw a picture of their prayer, sing it aloud or write it in a poem. These are all wonderful ways to express prayer that everyone can join in on.
There are several examples in the Bible of the Children of Israel coming together for prayer and fasting, from the oldest to the youngest. They all called upon the Lord together. Parents are admonished to teach God’s ways to their children at all times. And make a study of the different types of prayer and how people expressed their individuality. Even a two-year old can pray simple prayers, even if they are repeated, until they can express their own thoughts.
Expect everyone to participate. Give opportunities to all. Anticipate what God will do in the hearts of your children as you encourage their prayers. If you expect more, they will rise to it.