You of all people should know better than creating multi threads, that are related.

The DirecTV remotes are paired to the receiver they are controlling. Why would they connect to anything else? The Zigbee that the DirecTV remotes use, is a special subset of Zigbee (direct connection). They do not work with some other Zigbee products (like extender nodes).

The Video Bridge has nothing to do with this. The Video Bridge is the WiFi hub (5GHz) that DirecTV uses to connect the wireless clients to the Genie (server). You do not get very good range from that POS, so if the Video Bridge is installed at the opposite end of the house as your other thread says, there could be problems with the wireless clients connecting and getting video - from time to time.

And lastly... How do you think you are going to extend the antenna for the DirecTV Zigbee remotes? The existing antenna is internal and there are no external connections. So unless you plan on going all McGyver and solder your own connections on the circuit board, it is not something I would recommend trying. Also, as soon as a DirecTV guy shows up for some problem and sees what you have done; he will automatically blame you for whatever the problem might be.
Batteries dead in remote... "That guy that put the wires in the box caused it".
Access Card lost authorization... "That guy that put the wires in the box caused it".
Squirrel chewed the cables at the dish... "That guy that put the wires in the box caused it".