I dont own a Droid myself, and do not claim to be a Droid expert, however, video in general is something I am pretty good at. I seen your post since yesterday, so I figured I'd at least give some pointers.
The first thing I would suggest to try is to see if the file would actually play on your Droid. Rather than spending a considerable amount of time figuring out on how to get the file to save to your device, try and transfer the file from your wife's phone to yours (probably using a computer connection to her phone first to get the file, then a computer connection to yours to transfer it over.)
If the file plays, it might be just as simple as to visit the gmail website (not through an email app) using the browser, and try and access the file from there. It might play directly, or it might offer to download it.
If the file does not play, you might have to adjust some settings on your wife's phone for the recording of video (quality/format, whatever it has) and try the manual transfer again.
Most phones record in MP4 and/or 3GP format, and both should play fine on your Droid, however, it might save you a lot of hassle if you at least make sure the files would play.
Edit: when you visit gmail.com using a mobile browser it will load the mobile version. If that does not show the option to download, try switcing (somewhere at the top) to the "full mode"
