How terrible! I definitely remember when Ray Ray had those puppies and what a tremendous help you were and to be treated like this after all you've done for them, I just can't imagine. My vote is to go smack him and you can be gentle - or not
Unless your neighbor is willing to do something on their side of the fence, I don't know what else you can do. Like you said, you have to look out for your precious girls so you don't want to put anything down that could hurt them. I don't know how expensive it would be (you might can even find some scraps at a lumber yard or a home being built or remodeled) but what about plywood? You could dig down so many feet, stand it up, then cover it back up and no one would ever see it. Then when the dogs dig, they'd have to dig to freaking China to get in your yard. Of course, that may be way too much work but maybe when your sons come for a visit, they could help you with that. Wish I lived closer to you - I'd be over there today when I got off work helping dig it out.