On the topic of children and house church I have offered this quote before from Wayne Jacobsen before. I think it's extremely insightful:
But don't our children need church activities? I'd suggest that what they need most is to be integrated into God's life through relational fellowship with other believers. 92% of children who grow up in Sunday schools with all the puppets and high-powered entertainment, leave 'church' when they leave their parents' home. Instead of filling our children with ethics and rules we need to demonstrate how to live in God's life together. Even sociologists tell us that the #1 factor in determining whether a child will thrive in society is if they have deep, personal friendships with non-relative adults. No Sunday school can fill that role. I know of one community in Australia who after 20 years of sharing God's life together as families could say that they had not lost one child to the faith as they grew into adulthood. I know I cut across the grain here, but it is far more important that our children experience real fellowship among believers rather than the bells and whistles of a slick children's program.
