Answer: Round Up should take care of the plant so I'm wondering if new seedlings are popping up week after week. In any event, digging the roots of the trumpet vine out will help stop it. Any roots left will attempt to sprout and as long as you keep cutting the new sprouts down, the roots will eventually run out of energy and stop sending up new sprouts. For right now, I think I'd cut the stems of the plants at ground level and paint the cut ends with full strength Round Up. The herbicide should be transported up the stems and down into the roots and kill them all. Wait a week or so and then clear the ground near the foundation, digging the roots out as you go. With perserverence you should be able to eliminate the pesky vines.
Good luck with your project!
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