Question: How can I prevent trumpetvine from sprouting up all over my yard?

Answer: Native trumpetvine is notorious for sending up sprouts from its roots even as far as 25 feet from the mother plant. About all you can do is to encase the mother plant with some type of deep barrier 18 to 20 inches into the ground several feet away from its trunk. Then you'll have to hand-dig and remove all the now-severed sprouts or spray them with a broadleafed weedkiller containing 2,4-D in late spring or early summer.