Transfer downloaded iOS7 installer to home computer
You need to start by being aware that each different model of phone has a unique package for the iOS upgrades. So if you and your wife are not on the same model phone and the same carrier, there is a chance that your download won't work on her phone.

Assuming that you are on the same model phone (the size of the phone in GB doesn't matter), and if you are downloading your update via iTunes, then it will be stored on your computer somewhere. It will depend upon whether or not you are on a Mac or a PC, and which version of everything you have. A hard drive search for something like iOS_7* or ipsw should turn it up.

Copy that to your USB drive, and then copy it to your home computer. Open iTunes on your home computer with your wife's phone connected, and press and hold "Option" key on the keyboard (for a Mac) or the "Alt" key (for windows -- I think), and click the restore button. When it prompts you to a file, point to the file that you copied off of your USB drive.

Make a backup of the phone first. This method will cause iTunes to wipe the phone, and then you will need to restore it.