Setting up an expanded wireless network

We will need more information to be able to provide the correct instructions to do what you ask.

1) We assume that you already have an AirPort set up as your "main" router, correct?

2) Will the second AirPort connect to the main AirPort using a permanent wired Ethernet cable connection? This is highly recommended since it provides the fastest wireless performance.

3) Will the second AirPort connect to the main AirPort using only a wireless connection? While this will provide a network with more range, unfortunately the entire network will slow down......although this might still provide the help that you need.

4) What device will you be using to configure the second AirPort? A Mac? An iPhone or iPad?

So, if you can provide answers to questions 1-4 above, we can likely help. We will try to avoid asking you for model numbers, etc., but if there are difficulties, this might be necessary.

The TV should not get "kicked off" if the second AirPort is set up correctly.....since an extended network is producing the same wireless network over a greater area.

If the TV is located near the area where you plan to add the second AirPort, it should pick up a stronger Wi-Fi signal. To do this, you will need to power off the TV once the AirPort network is up and running and then power up the TV again so that it will pick up the signal from the closest AirPort.

But......after all the "shoulds" here, there is really only going to be one way to see if things "will" work.....and that is to try them out. Wi-Fi has always been half science and half voodoo. Worst case, you power off the second AirPort in the very unlikely event that it messes things up.

The TV is located directly opposite the Airport Extreme router that is my main wireless connection to the Internet.

Then, the TV will continue to connect to the main AirPort Extreme.

The second airport will be set up in a room at the far south end of my house, about three rooms away.

That is fine as long as the second AirPort will connect back to the main AirPort using a permanent wired Ethernet cable connection.

Not fine though if you are planning to connect the second AirPort using only wireless. in that case, the recommended location of the second AirPort would be a point that is about half way between the main AirPort and the area where you need more wireless signal coverage.