airplay requires both devices to be on the same network, so wireless for the ipad, wired/wireless for the aTV.
you might be able to set up a router, with no internet, that would let you play files stored in memory on the ipad, but it would take some fiddeling to get it to work, so not ideal in your situation.
you would only be able to connect to either the 3G or the aTV, but not both at the same time.
if their TV has HDMI in, you can get a cable that will put the ipad screen on the TV. it's available with either a
lightening or
dock connector
and would be a better fit in this situation.
you can get a long HDMI cable if they still want to be able to use the ipad on the couch.
check
monoprice.com for the cables, they have great prices, and good quality cables (25 foot cable is around $20, shorter are much cheaper).