Using my MBP makes my router stop working.

Are you connected via WiFi or Ethernet cable (or something else?)

 

Is every device's connection to the Wi-Fi getting disconnected or just the connection to the internet? Have you tried connecting a device with an Ethernet cable and see if that still disconnects the computer?

 

What IP address is your MBP using? Check in System Prefs > Network > WiFi > Advanced > TCP/IP. It should probably be set to "Using DHCP" so the router can assign details to you.

Do you ever get warned that your IP address is in use?

Probably completely wrong but worth checking!

 

This happened to me the first few times I synced my iPhone wirelessly. It would "shutdown" my router and I would have to power cycle it.

 

I've been having a similar problem. A few times when I've been using my MBP I lose my wifi connection. The router continues to function (others connected to it via ethernet don't lose their connection) but I lose my connection to the internet even though it still shows that I'm connected to the router via wifi. Other devices connected to the wifi also lose their internet connection. When I reboot the router I get the error that another device is using my IP address.

 

If you have access to the router control panel, go in there and find the DHCP allocation area. Assign static IP addresses to all the "normally" connected devices.

Sounds to me like a device is not respecting DHCP lease times.... assigning permanent IP addresses should help with that so that none of your devices ever try and use the same IP.

Also, ditch the ATT Router. Junk.