I have a desktop PC that I prefer for gaming (better in all areas), but I also have a laptop that I wanted to put Skyrim on for long trips I have to take. Are we able to get it to install on more than one PC as long as they're not played at the same time?

I don't see why not, just make sure your laptop can be connected to the interwebz as you need a connection to Steam to verify the game and look for updates. Inbetween I would select off-line to play.

Good luck.