I have more of a cat that forces me on adventures. But she thinks she is a dog anyway, so that must count. Is a MinPin a miniature Doberman? Looks like it from the south end.
One thing you can do to alleviate the fence digging, is to attach a small-hole wire fence along the bottom, and then turn it to an L, which is buried about 3-6 inches underground. Does that make sense? I can make a diagram. But they dig, but can't get under. At least it works for Nutria and raccoons, etc...so why not for dogs? Though leaving the gate open, kind of negates your gained ground a bit ( :
Plus, she may be smart enough to keep digging BACK, until she hits below the horizontal wire. Probably much smarter than a buck-toothed Nutria.