Thanks to all who posted. FYI, I'm not trying to "cheat" on my license (which is legal) -- at least in any way that would harm the company -- I'm simply trying to allow my daughter to learn on her own computer in the evening when I'm not working, although I don't want to go through the hassle...
Certainly does sound like a bug to me. Step 1 would be to contact your VAR support team to see if they have seen this before. I've found they can sometimes guide me through some pretty tricky stuff that would not be obvious to the average SolidWorks or Windows guru. Failing that, try either...
I skipped from SW2005 to SW2009, and somewhere in between began the polling of the license server to assure that the license is valid and not being used more than once or installed more than twice. Does anyone remember what release that started with?