Yes, I do realize that, especially since there are other dogs on all sides of us which she loves to bark at and run back and forth with. We thought of hedging, but besides being pricey we think that she'll just make her path on the other side of it intead.
I really don't like the concrete idea, because I'm afraid of that too (plus I don't want a concrete perimeter around our yard, as I'm sure you can understand). What if we dug out a few inches, filled in w/ landscape fabric, crushed stone fill and then river rock, mulch, et al over that? If we bordered it up high enough (say with stone edging) would that keep the material in place?
And, more importantly, do you think that our wonderful dog will still choose to run in there as opposed to making a new trench on the other side of it?
You could try the stone path thing but I doubt it's going to solve your problem . You could you try it on a small section and see how she reacts to it . If it's uncomfortable on her feet , she'll just run down the outside edge and create a new mess . Large dogs and yards are not compatible . Been there , done that .