For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
I have not seen the Bible study but did read the book "Praying Circles Around Your Children". As long as you are praying to our one and only true God you are safe. The Bible encourages us to pray for each other. Even Jesus prayed for His disciples. You should pray for your family, children, each other, the church, and the plight of other countries. I see nothing wrong with gathering with friends or family and circle your children with prayers of love for safety, healing, health, their own belief in God and for the Godly path they will be called in their lives. Prayers to our God are always Biblical. Go for it.