[[ The drive is bus powered. When plugged into the MBA the light does come on and it seems like it powers up just fine. ]]
Again, even though the light "lights" and you hear the drive spin, that in itself may not be enough. Again, it might still be a "not enough power" issue.
Does the drive have a "port" to accept an external power source?
Are there any voltage settings specified?
I would try a "universal" power supply (can be found at places like Radio Shack, online, etc.) provided I knew the required input voltage and had the right fitting.
You can probably find one of these for around $10-15.
If you're not willing to try that, I would at least try the drive on a couple of -other- Macs than yours and your wife's. Do you get the same results (fails to mount?).
In that case, I'd start looking around for another drive....