Harry,
Go to K-Mart, Home Depot, Lowes, and your local garden center and tell your problem to just about anybody working in the "lawn chemicals area." It is advisable to get multiple opinions, especially at K-Mart type stores. :)
There are many products which will somewhat selectively kill poison ivy. You can purchase the chemicals in bulk for use with a pump sprayer or you can buy individual aerosol cans (about $4-$5 each) for spot application. I believe that Ortho's aerosol cans have pictures of poison ivy, poison oak, etc. on the front of the container for handy reference.
Some standard broadleaf weed killers (eg: dandelion killer, 2-4-D, etc.) will attack poison ivy somewhat, but there are much better specific killers for so-called bushy weeds such as poison ivy.
Also, you can use just about any broad-spectrum herbicide such as Roundup. Keep in mind that these products kill just about any plant whose leaves they touch and you can't easily use them to kill a weed which is among favorable plants. If you spray them on poison ivy which is growing up a tree, then the overspray onto the bark of the tree is not a problem. In some areas you may have to "bite the bullet" and use a broad-spectrum killer to kill everything in the area just because the broad-spectrum killer is much less expensive and more effective.
Also, do some "Google searching" with search arguments such as:
"poison ivy" cashew mango
This should give you some EXTREMELY important advice about foods which your wife should avoid while recovering from poison ivy contact. There are a number of fruits which come from plants which are closely related to poison ivy. The levels of allergens in these fruits is normally not a problem, but they will greatly increase the allergic reaction to poison ivy. Recovery from poison ivy contact is slow and uncomfortable - don't exacerbate it by eating the wrong foods which contain small amount of the allergen that causes the poison ivy reaction.
If you have a lot of poison ivy on your property, then you probably won't knock it all out in your first attempt. Do some "Google" searching to learn now what you or your wife should do to prevent future contact or to deal with future contact. Poison ivy oils can definitely migrate into your house on the fur of your pets. There are established procedures for washing poison ivy oil from skin and clothing after contact. All of this information and more is easily accessible on the Internet. Just do some "Googling" with intelligents search arguments.
Good luck, Gideon
PS: Thanks for mentioning that you are aware that the subject is somewhat off-topic in this newsgroup and thanks for complimenting our little newsgroup. We try harder.