I had an idea a few days ago but I have no idea if it will work.

My idea was that because NXT bricks have built in bluetooth, that because my team do not have any bluetooth dongles, that we could possibly use another nxt brick to send information through bluetooth, but the information is from originally a logitech controller which is plugged into out computer.

If that didn't make much sense here.

So it goes from Controller to the computer, to the NXT Brick connected by USB to the NXT Brick that is in the Robot.

Is the idea possible and if so, how would the programming look?

Why make it so complicated? You can get a Bluetooth dongle for $8 (no tax and no shipping). I bought 5 of those when they were on sale for $5 a piece. Even now, $8 is not bad.
http://www.newegg.com/Product/Product.a ... -Bluetooth
To communicate between NXT bricks using Bluetooth is not simple. You have to write code to do that. Besides, for FTC competition, you are not allowed to turn on Bluetooth anyway. BTW, you don't really need Bluetooth, you can use WiFi to talk to the brick using Samantha module.