I agree with you 100%.... call your friend and see what she can find out...i.I know you don't want to alienate your new neighbor 'but'............maybe invite her over for coffee, and have a talk with her...let her know how frightened you and Dex and hubby are of the Rot...
We've got a similar situation at our place in NH...'George' the Weimarner is constantly on our property, pees on the vegetables, poops where he pleases, gets into the garbage if the garage door is open, and drives Molly and Raleigh nuts!! We installed the invisible fence, so that our dogs could run and have a great time up north...
P.S. We've called the police 4 times, who in turn calls the dog warden...we've seen the people in person twice, asking that they keep George contained...the second time we gave them a $50 gift certificate towards an invisible fence....still George is roaming....their neighbors have even shot paint balls at him, whch I don't like, because it's not George's fault, it's the gosh darn owners!!! Who by the way obviously have no regard for their neighbors, or property...THERE...sorry I vented, and I wish you luck...because we certainly haven't had any...luckily, George is quite docile...