Yes you can do it, but it isn't something supported by Directv so you can't get them to install it that way.
How do you have the wifi link from the house to the barn set up? I assume you have a wifi router in your house, and another wifi router in your barn for the other end of the bridge?
If that's how you have it set up, you'd have Directv install your house with one more TV than you need (i.e. some spare TV you don't plan on getting Directv for, or moving the barn TV to the house temporarily) Make sure that extra TV is set up as a WIRED client, not wireless!
Directv's clients have a coax connection only, you can buy something called a "DECA" for a few bucks off eBay (
DIRECTV DECA RECIEVER (GREEN LABEL) PWR INCLUDED FREE SHIPPING!! | eBay) that is an ethernet to coax network bridge. You connect the ethernet end of the DECA to the barn wifi router, and the coax end of the DECA to the barn Directv client, and plug in its power supply.
Directv will install your Genie (main DVR) with an internet connection, it can be either wired or wireless, doesn't matter either way it will connect to your house's router. That will allow the communication between the Genie and the barn client to run over your wifi bridge when you move that client (initially installed in your house temporarily) to your barn and connect it as described above.