When Christians depart the institution they leave the fun and games behind. In simple church life the kids tend to be right there with mom and dad regardless of what is happening. This can be during bible study, eating, or whatever else. If the kids are used to church being full of fun and games, they might long for a return to institutionalization. Likewise, if mom and dad desire more peace and quiet, they too might want to go back.
The reality is that simple church life can be messy. Kids are messy. They are active and they are loud. They are also awesome to have around because of their energy and vibrancy. If a small group embraces children as a real part of the group then wonderful things can happen. The kids benefit from being part of everything that is happening. The older folks benefit from the kids' enthusiasm. As the apostle Paul tells us that the entire church is a body; the kids are part of that body. The church needs them.
Parents, I strongly encourage you to resist the temptation to go back to Rome for the sake of the kids. They don't need any more church entertainment. It's your responsibility, with the assistance of the church family, to raise your kids in the knowledge of the Lord. There's no better place to do this than in the small group setting. Children gain immeasurably from watching and listening to their parents as part of the group.
Even if your small group has no other children, your kids will be fine. They will learn better how to be around adults. They will not suffer from not being with other kids when the church gathers. They don't need to make more crafts, play more silly games, or watch another lame video. What they need is to be with mom and dad as the body gathers. Keep them with you and resist the pull of the institution.