I should have read more about poison ivy before I tackled that vine in the back. (Which looks like it almost certainly was poison ivy.) Don’t pull it out by the roots. Don’t take a hot shower afterwards. I don’t have any sign of a new rash yet, but I’m not sure how long it can be.
And how to get rid of all that? Sounds like the best approach will be to cut it off regularly until it gives up, which it says can take several years. (And what to cut with?) Looks like I’ll be keeping the kids away from the back fence for a long time.