I have been listening and reading stuff from the guys at www.ids.org for over a year now. They are New Covenant Theologians who have a passion for Reformed Baptist Theology. I absolutely love these guys, they have been such a blessing to me. Here is a paper they wrote on how to deal with your nonbelieving children in the context of Church. They bring up some very interesting points, that I really never even considered. Here are a few.
1. We should not let our children lead worship (you know children choirs) unless they are believers.
2. We should not treat them as believers (i.e Lord's Supper, serving in the ministry, and other church related functions).
3. We should not let them lead prayers, for they are nonbelievers (unless of course that is a prayer of repentenance)
These are just a few. I had a few objections that I emailed them about and I am waiting for a response. As for now let me know what you think. God bless.