ew ew ew... I'm so sorry to see that rash
My husband gets *horrible* poison ivy, and it looks just like that. In fact, one mild winter he had it nonstop from March one year to November the next year - 20 months nonstop. The pets bring it in regularly, and deposit it on the backs of his legs when they rub against him.
The advice from PPs about the vine in question is very good, and I won't pretend I know anything more about that
But, I'm willing to bet the culpret was the poison ivy your husband destroyed. You phrased it that he "weedeated" it. Do you mean he used a weedwacker? Bad, bad, bad ugly mistake. My husband did that once, before I had the chance to warn him of the folly... weedwackers spew shredded plant bits *everywhere*. And the oil (urushiol) that causes the reaction is very tenacious - it'll remain on the surface of dead plant bits for a long time, laying in wait for a hapless victim.
The rash takes a couple of days to develop. My husband finds it takes approximately two days after exposure to develop the rash. I'm willing to bet that your rash was poison ivy from your hubby's eradication effort. It might have been deposited on the vine you were pulling, or any other plant or gardening implement you were using.
So, never ever weedwack poison ivy!!!!! If you only have a little bit of it, put on plastic gloves and long clothing and pull it out of the ground. You'll have to do this several times until you succeed in killing the roots. Do *NOT* burn the vine - you can end up with the rash in your eyes and lungs, and you can die from that.
After three years of battling our literally acres of poison ivy, we finally gave in and started using non-organic means against it. It went from a question of organic gardening to a question of health care. We came to the realization that eradicating it once with Ortho would ultimately have a lesser impact on the earth than my husband having to take (and pee out and so forth) steroids for the severe rash several times a year forever. We felt seriously guilty about that until we heard from a friend, who has a PhD in botany and is a die-hard organic gardener, that Ortho's Weed-B-Gone is one of the least harmful herbacides you can use. It's very tightly targetted and it breaks down in the environment very quickly. With his seal of approval, well, we now only feel a little cheesy. However, I will only recommend that if you have *way* too much to reasonably pull by hand. Even at that, if it's a lot but manageable, you can cut and treat the exposed stems individually and never put it into the soil at all. I've heard of two different methods for this - painting it on with a paintbrush, and putting the stuff in a soda can and putting the cut stem into the can, taping it in place and leaving it there. I've had luck with the paintbrush method, but I'm not kidding when I say we have acres of it. I spent an entire day and made it through one garden bed, which was maybe 1% of our total poison ivy load, and 5% of the most dangerously, publically placed poison ivy...