Hello
Oshi121 - from my understanding of your question, you are plugging the USB portion of the iPad's charger into your DirecTV box; well the iPad is not going to put out a video/audio feed via that connection - could the connection even damage the iPad? I'm not sure - I believe that you will need another of the many options for getting iPad video onto a bigger screen - both wired & wireless choices exist.
For myself, I own the Apple HDMI video adapter (of course other third party ones are available) - as you know, the HDMI is a great option being just one cord that will carry both HD video & audio. However, there are many other video adapters (again either from Apple or third party providers), e.g. composite, component, VGA, S-video (did I miss any?) - for the latter you will also need to deal w/ getting the audio into whatever device you are attaching.
My suggestion is if you already own an iPad HDMI docking adapter, find or purchase another HDMI cord - good luck!
P.S. welcome to the forum!