The suggested lenses are all fine, but not all of them are wide angle. If wide angle is what you really want, then I think the less expensive end of the list is pretty short:
Sigma 10-20mm f4-5.6 I've linked to a new one from a reputable dealer. There's at least one other version of this lens that's about 45% more, that you don't need. This lens or one with similar specs has been around for a while so you may find a used one on eBay. Just make sure it has a Pentax mount and it should work on a K-x.
Tamron 10-24mm f3.5-4.5 This one has only been around for a few years and may be tougher to find used. The specs look a little better and it has a bit more range, but those aren't going to matter a lot because your wife already has something to cover that range. It may be harder to find used.
Bower 14mm f/2.8 This is a single focal length lens. It's still a wide angle but can't be zoomed to adjust its focal length. It's also manual focus. I think a zoom lens like the above two are more generally useful, this one is more specialized. Samyang makes it, but it's sold sa a Samyang, Bower, Rokinon, Vivitar and maybe some other names, all the same lens. This one is also newer so maybe less available used.
Wide angle lenses for DSLRs are just not cheap.