If you are going to set poison ivy and grapevine back much, it would need to be twice a year, spring and late summer/early fall.
I'm not a fan of poisons either. But poison ivy is about where I draw the line, since I'm very allergic to it. I can't weed whack it, because all those little particles flying in the air would have me in painful, itchy rash anywhere they managed to find skin. There's a couple alternatives. You can clip the poison ivy vines (well gloved up) a few inches above ground and then immediately paint the clipped end with RoundUp painted on with a brush. RoundUp is still a poison, but one of the safer ones as far as people and pets are concerned and painting it on instead of spraying limits the environmental damage while concentrating the effects.
If you are resolute about the poisons, you can try treating it (painted or sprayed) with a concentrated solution of vinegar and salt. It will definitely kill the foliage, but less likely to be taken up and kill the roots.
For vines growing up trees, you can't weed whack, you have to clip them at the bottom and then pull the now unrooted top part off the tree. They send roots into the bark, so have to be pulled loose.