Invasive weed question 1: What's the best way to get rid of poison ivy?

I’ve never had it growing in my yard until a few years ago.

The issues are:

1. I tried get rid of it a couple of years ago only to discover that at some point in my life I have become allergic to it and now, like other people who are allergic, I would prefer to stay as far away from it as possible.

2. I don’t use pesticides or herbicides, or any ”-cides” with the one exception: I have a scorched earth policy regarding yellow jackets. I will drown them in toxins; I would use tactical nuclear weapons against them if that’s what it took. So … I don’t really know that much about herbicides and what to use on the poison ivy.

3. The locations where it is growing are a problem. Some of it’s pretty isolated and I can see where it’s rooted and I could attack it at a distance if I could spray it with something. In other places it is growing among and around things: trees, shrubs, my day lilies, e.g. Can I get rid of it without killing everything around it? And am I going to need to find the roots? In some spots I can’t see where its growing from because it’s mixed in with everything else.