I have a Dish 2 tv output DVR with one HD and one SD signal. "TV 1" signal is HD. "TV2" signal SD.

We are installing a second HDTV. Is there a way to switch that TV which picks up the TV2 signal to TV1 HD signal when the other TV is not using that signal?

DIsh makes it sound like I have to switch the coaxial output which is impractical every time you want to use the HD signals. Can this done with the remote? If not what other solutions are there?

You can't pass HD from the DVR to an HD set over the standard Coax output you currently send to TV2. You'd need to manually swap the HDMI or component output between the two sets, split the component using a distribution amplifier or if the box can output both component and HDMI at the same time, run HDMI to one set and component to the other.