Do you have a picture? There are many plants that look like poison ivy. While it is possible for poison ivy to grow as a low shrub, such types don't usually get over 4 feet high. Bladdernut and hop tree have leaves that are similiar to poison ivy. Can't think of any trees that get very big with trifoliate leaves though.

Box elder (Acer negundo) trees look just like poison ivy to me. See the link below for a photo.

Here is a link that might be useful: Box elder photo

Is the PI growing up a tree trunk or stump. Here in the North East it happens all the time. I see it a lot on wooden fence posts along farm fields that have been let go. Rural utility poles also become great columns of this scourge. Worse yet when it branches it also flowers & sets fruit. Of course most birds love the fruit & you know what that means, welcome to the garden. Ortho's Brush be Gone or Gordons Pronto Brush Killer works well at doing it in. Also if you have vines on a tree or back of the barn etc. Use an axe or machette to chop a minimun 2" piece out of the vine. If it is just cut and the two pieces touch, they will connect themselves, the sap will seal the ends together and continue growing.
Have a wonderful itch free rest of the Summer.
Frank

Here is a link that might be useful: P.I picks