You’re right on both counts.
Port forwarding usually has nothing to do with monitoring other computers on your network. Port forwarding is commonly performed by the router so servers on the Internet can communicate with specific computers on your network without being blocked by the firewall. Or so servers on your local network can be accessed from the Internet. The most common use is to open specific ports for gaming.
You can use GlassWire to monitor your kids’ computers. The free version only allows you to monitor one remote computer but the paid versions allow more. See the comparison chart in this post: