pardon my ignorance, but how does dish do it?
Uhhh Unless it is a bank vault then it can be done. Either a wall fish, through floor, ceiling, windows, under carpet......haha
That small 6" antenna is probably the RF receiver that just receives the remote signal, not the signal from the satellite itself.
DirecTV has the RF antenna built into the receiver, if you have an RF remote (R at the end of the model number on the top left of the remote) you can switch to RF mode in the setup screen.
If the RF signal is too weak to reach the receiver there is no easy solution other than relocating the receiver. Also try new batteries if this is the case.
You can try something like this coming from the RCA ports on the receiver, but the quality on these things sucks, reviews are always bad. Sending wireless video is not a good solution, you'd be better to pay the $6 for a second receiver before doing this.
Amazon.com: 5.8GHZ Wireless Catv Sender: Electronics
That X10 unit is the same technology as the link to the one on Amazon. Just cheaper.
Also, note that since it's wireless there may be interference with other wireless equipment (cordless phones, WiFi).
I'm not sure what if anything can do it pre-receiver, but I would highly recomend not wasting the money/time on that one. The ones for after-receiver work terrible, pre-receiver would be even worse.
You are best to find another seutp. What you saw at that girl's house had to have had coax involved, the small antenna just was the RF remote receiver. Dish receivers have a modulated coax out for other TVs, but the DirecTV receivers do not. Even on the dish setup you would have to run coax.