In reply to The Lemming:
And in terms of other devices, block them from the network.
Chances are, the router will have a security option that will either only allow certain MAC Addresses to access the network, or can block certain MAC Addresses from the network.
A MAC Address is a unique address that all computers/phones/network devices have that identifies it. The most secure method is to block all addresses but the allowed list, this helps prevent ANYONE else from accessing the wireless etc, though if the network needs to be shared then the second option for blocking certain devices may be applicable.
Can I also add, this is for the purpose of preventing the children getting access through the wireless, and ADDING security to the network. You should still use the wireless encryption that you would normally use to secure the wireless!
If either child manages to bypass this security, then I would suggest you might have more to worry about