One thign to remember with RoundUp - read the fine print.
At my local HD, there are gallon jugs for sale with the word "ROUNDUP" in the largest letters they can possibly fit onto the label. Plus some salesy verbiage.
Then the fine print, like in 8-point font on ther back label or glued UNDER the label, shows that BESIDES the glyphosphate (which is what Roundup means) there are ALSO other chemicals that you need a magnifying glass and Google to figure out.
Sometimes those are benign (like soap that helps that helps the glyphosphate cling to and enter the leaves). Sometimes those are much more toxic than the glyphosphate.
I think they do it that because everyone wants something minimally toxic to animals (hence ROUNDUP in huge salsey letters on the front label).
But everyone wants something as effective as possible, hence the really toxic additions.
Ya gotta look close when so many vendors seem to go to the Ferengi School of Business Malpractice.
Maybe pull up as many vines as you can, then use a torch on the remaining above-ground parts, then use a mattock on the roots you couldn't pull. I would expect that to reduce the amount of ivy over a few years.
I have a lot of ivy growing around big old pine trees, and I periodically pull them down from the trunk and pull and cut them at ground level.
I don't really ever expect to get RID of the ivy.