Thanks for your quick response and explanation. I don't know why they allow you to install it on two computers if you can't use it fully on both. The issue is in the version control, which should be simple enough since this is already handled when synching the ancestry web site version with one copy of FTM.
I use Dropbox extensively but would consider it "dangerous" to rely on a cloud-based service as the working directory for a primary file. For example, I know some people that use it to synchronize their Outlook pst file between two computers. Both computers read/write to outlook.pst in a directory in Dropbox and the local version on the hard drive.
I guess I should just be happy I have it working on one of my computers!