Xbox One will not allow me to enter network settings

You can't . Once you disconnect you need enter the password again.

Xbox One doesn’t save old device information, allowing you to completely wipe out old settings and start new each time. This saves you from accidental manual entries that could cause issues on a new network.

http://support.xbox.com/en-US/xbox-one/networking/network-settings

Sorry I missed out a vital piece of information - To get the wireless Xbox one to stay connected I had to enable one of the four 'guest' wireless connections on the router and dedicate that connection to the XBox one. Running the XBox on the main wireless
network caused it to disconnect if any other device connected, running it on its own dedicated guest connection allows it to stay connected until I enter a multiplayer game on our other Xbox One which is wired to the router.

The router doesn't seem to allow me to set a static IP Address for devices connected to the guest wireless networks, only the main wireless network.

EpicPoodleJTC, an alternate MAC address is when you take the MAC Address of an already connected device (Every network connectable device has one), and you enter it on the Xbox One under the Advanced Settings. The network sees the MAC Address and it tricks
that network into thinking the Xbox One is the other device, thus allowing it to connect to the internet if the other device has accepted the terms and is able to get online.

Sounds like what bren 2003 said would be your best bet. You need to use mac filtering to make your router only allow certain mac addresses to connect. The xbox one can have the mac address spoofed. Ever see the spot were you can enter an alternate mac
in the network settings? That's where he is spoofing it. Unfortunately one of the things you asked was if you could avoid having to enter your other 12 devices. With this you would have to enter them. I looked through the setting on my own kids stuff and could
not find a way to restrict then from the network settings on the xbox. Kinda shocked me. So no I don't think you can avoid listing the devices in your router.

My Xbox One can't sign in. It doesn't even allow me to enter settings. And when i'm trying to reconnect the screen becomes dark for a while and nothing appears...