Before anyone can visit, they have to be on the inmate's approved visitor list -- this includes kids.
How the list actually works
The inmate requests a Visitor Information Form from their unit team and sends a copy to each person they want approved, including any children. That form gets filled out and mailed back to the facility, and staff review it (sometimes including a background check) before adding anyone. This can take real time -- weeks, not days -- so start the paperwork as early as possible, not the week before you want to visit.
The rule that trips people up: kids under 16
A visitor under 16 must be accompanied by an adult who is also on the approved list. If that accompanying adult is not the child's parent, legal guardian, or an immediate family member 18 or older, you'll need written approval from the child's parent or legal guardian before the visit -- have that documentation ready, don't assume you can sort it out at the door.
One piece of good news: kids 15 and under don't count toward the facility's visitor-count limit for that visit, so bringing multiple children generally doesn't use up visitor slots the way adult guests do.
Every facility can add its own rules on top of this
These are the baseline BOP rules, but individual facilities can be stricter about documentation, hours, or how many total visitors are allowed at once. Check the specific facility's page here on InmateForum, or call ahead, before making the trip.