The Tiagra cassette is likely the largest cassette that can be run on your wife's 105 derailleur. It's a cheap upgrade and could be a nice cassette for you if you want just a bit lower gearing.

The other option pointed out is a Shimano mountain derailleur (like the Deore linked) and a mountain derailleur (like the SRAM 12/36). The one thing to note is you need a 9 speed Shimano mountain derailleur, as Shimano 10 speed mountain derailleurs have different cable pull ratios. A 9 speed mountain derailleur should work fine with a 10 speed road drivetrain.

A triple probably wouldn't be a terrible idea (better shift patterns, closer ratio spacing), but it would cost a lot more to upgrade.