@Concerned, step back and start from the beginning:
- you have Wireless router
- you have DirectTV DVR. How is this DVR connected to the router - wired, or wireless? If wireless, how far?
- you have a PC you want to watch DVR with. How is that PC connected to the router?
TV tuner and cable have nothing to do with the problem you have. With TV tuner, you can watch over-the-air TV channels with appropriate antena, and appropriate software for your PC. You could probably use that TV tuner (connected with coaxial cable to DVR' TV output) to watch TV as well, but that is completely different solution to your problem. And then, how you will change channels?