Alright, I have to say, I am impressed with myself! I installed Win 10 on my wife's Win 7 computer without a hitch! I waited a bit to post here just to be sure everything went smoothly. So far, so good.
I did some research here in the Windows Forums. In the "Windows 10 Upgrade and Installation" Forum, there is a thread titled "Getting Windows 10 for an Older Build". In that thread, livix07 provided a link titled "Download Windows 10 Disc Image (ISO File)". The link requires you to first download the Media Creation Tool. I did this and somehow read, I had to have either a new clean DVD or USB zip drive for the download. So, I had a new Zip drive plugged in. Turns out, if you are on the computer, you are upgrading, you can start the upgrade right then. There is no need for the external media.
I found, the key to success is patience. I did it later at night, assuming it was going to take some time. It did ... a couple hours later, I had Win 10 on her computer. Nothing (old files and programs) was lost, everything (so far) still works. Just had to take the time to do a few checks for updates in "Windows Update" and get it all up to speed.