Yes, there are ways to control the poison ivy growing up the trees. To do it safely you will want to wear protection and be careful. During the active growing season of summer, a chink in the vines can be cut and immediately painted with a type of weed killer. Don't tear off or try to remove the vine, that will degrade on it's own.

This page from our website has more detail for you: https://extension.umd.edu/hgic/topics/poison-ivy

Christine

You do not need to pull the vines off of the trees. You can cut the vine at the base in the winter.  However, in the spring or growing season there may be new growth where you made your cut. 

Keep the new growth either cut off or make a fresh cut and immediately paint an herbicide such as glyphosate or triclopyr (brush killer) on the stem (when the vine is actively growing). Follow label directions for control.  Do not get the herbicide on any plant that you value. Regularly monitor where you cut the vine at ground level throughout the summer and eliminate new growth if you do not use an herbicide. (It may be easiest to cut the vines and treat with an herbicide during the growing season.)

Even in winter, when the leaves are gone, you can come into contact with the berries or aerial roots and pick up some of the oils. See our webpage on poison ivy (control and ways to protect yourself). https://extension.umd.edu/hgic/topics/poison-ivy

Marian