Here is the source of your problem. When the Genie network is operating without the connection kit, the SWM dish assigns IP addresses to each receiver and DVR. When you connect the W CCK the router sees all of those foreign IP's and conflicts occur.
Disconnect AC power from all the Directv receivers except the one adjacent to the CCK. Hold the reset button on the back of the CCK-W for 30 seconds. Assure that DHCP is active on your router and no firewall is in place. Disconnect AC power from your router for a minute or so, then reconnect and wait for the router's lights to settle down. Then on your HD DVR press
MENU ➜ SETTINGS & HELP ➜ SETTINGS ➜ NETWORK SET UP ➜ RESTORE DEFAULTS ➜ CONNECT NOW ➜ GET CONNECTED ➜ WIRELESS. The receiver will then scan for WiFi networks and should find yours. Once it finds your SSID, select your network name. if your network is secured, it will ask you to type in your password. If successful, you will get a message that says "congratulations, your receiver is connected to the internet". Note that your SSID and/or password cannot have any spaces and/or special characters, letters and numbers only. Once connected, reconnect AC power to each of the remaining Directv receivers.