Hi Reg and welcome to the forum. So glad you found us. I took the liberty of moving your post to a different section where more people will find it, since you did have a question and not everyone reads the introductions.
To start with are you sure that it is poison ivy? That trick of coming in houses and smothering trees sounds more like regular English ivy. Here's a picture of what the leaves of English ivy look like:
Here's a picture of poison ivy:
The poison ivy leaves are always in sets of three like that.
The methods of control are different, especially since you can't TOUCH the poison ivy.
I have plenty of both on my property. The English ivy responds pretty well to being cut back and then stripped out. Cut all the stems where they start to grow up trees or into houses or other places you don't want. Anywhere above the cut will die and then can be peeled off once dead. Then after a rain or watering when the ground is soft, take the bottom part that is still attached and just start tracing it back, digging and pulling as you go, getting as much of the roots out as you can. You inevitably will not get all of the roots, but it does set it back pretty hard and if you keep vigilant about pulling sprouts that come back, you can eliminate it this way.... big job at first but I've done it.
The poison ivy though really I still use Round up on. The fact that yours hasn't responded to the Roundup is another argument that it's really English ivy which is tougher skinned. You can always try a repeat application.
PS Congratulations on your first house and welcome to the joys of home ownership!