What actually happened: moving the receiver
This is the update I promised about getting two sites with one receiver. This is to help naive users like me get up to speed faster.
Thanks to the good advice from this forum, I asked Dish for an upgrade from Family Plan + Locals with an old receiver and a Dish 500 antenna to Family Plan + Locals with a 612 HD receiver (with DVR) and a Dish 1000 antenna. Cost was an $100 one time fee plus $6 more a month for the DVR (with some extra taxes) and a 2 year commitment. Given that I have the DVR and some HD channels, this seemed like a good deal.
I then called Dish for their Snowbird/Move plan. For no more money, they installed another 1000 antenna at the other site. The receiver/DVR I now move back and forth works perfectly at either site. In fact, the standard definition reception is superior to what I had before. This might be a result of the combination of a better receiver, a more carefully aimed antenna, and improved wiring.
I cancelled cable service at the other site so for less money I have better television. I have purchased some duplicate cables so I don't have to carry those around. Note that Dish does not seem to care about this. They would like me to tell them the telephone number that I connect up to when I move the receiver, but for the moment that does not seem to be an issue. If I had gone for the 622 receiver, apparently, I would either have to always hook up to a telephone or pay an additional $5 a month to use satellite band width to download the information.
One surprise was the information the installer told me, that I cannot use my house cable system to send HD signals to other TV's, just SD. Perusing other discussions on this forum indicated that, with the receiver I have, I could connect a second HD TV shwing the same channel if one would be connected to the receiver with an HDMI and the other with component cables. There is some limit on distance, up to 50 or so feet. Alternatively, I could buy a powered HD splitter and send signals over two HDMI cables or even over pairs of Cat 6 cables. I can now think about this option.
One final note: the Dish installers at both sites were excellent: patient with my questions, careful with the installation of antennas to get an aesthetic (that is, hidden) location, and providing a good path for the wiring.
Thanks again to all for the key leads.