The DirecTV app for the iPad does not support streaming.
It only acts as a remote control and scheduler.
The DirecTV NFL Sunday ticket app is the only one that streams from the web. That will cost you $300 per year for that handy feature.
Also, DirecTV DVR's are not compatible with Airplay, so they cannot stream to an iPad or iPhone without some kind of a software upgrade.
Currently only DLNA equipped phones can stream to and from a DirecTV DVR.