Is there anything that I can spray on the vines & poison ivy that grows in my Azalea bushes that won't also kill the bush?
Nothing at all that I can think of.
If there was such a product, I'd use it on the periwinkle, blackberry, invading the stretch of cotoneaster holding up a hillside (about 10x85') in the gardens I'm trying to restore...
What people do is cut the vine at the base and leave a couple leaves. Then they paint the leaves and the cut stem of the vine with roundup. Roundup is then transported by the vine to its roots where it kills the roots of the vine. It does not kill neighboring roots, so it is safe to use this way. The roundup must not touch any green parts of the azalea or other desirable plants, since it enters the green tissue and will kill that plant also.
With vines, it is just about impossible to spray without hitting neighboring plants. Another alternative to brushing is to put on a cotton glove over a rubber glove and moistening the cotton glove with roundup and wiping the roundup onto the stub of vine under the desirable plants, avoiding any contact or dripping on the desirable plants. With nasty vines, they use strong concentrations of roundup or even the straight concentrate. That is quite risky since it will kill anything green it touches. If you haven't used roundup before, it takes about a week to 10 days to kill a plant. However if you get some on a desirable plant, you only have a couple minutes to wash it off.
Roundup is an interesting material. I have some large trees next to my driveway. The lower branches obscure my view of coming cars. To defoliate these branches, I spray these branches with roundup. It doesn't kill the tree. Since these branches are such a small part of the tree, it just kills the portion of the roots that are feeding these branches and these branches die and the tree remains healthy.
Many ivies and poison ivy have waxy leaves are are harder to kill with roundup. It takes a stronger concentration.