Minna digs too. I was down at our house that sits on 9 acres of orange groves and I always let the two dogs out back on a LONG (60foot) lead so that they can sniff around and move around a bit. And I'll walk in and out, make coffee, grab a bite to eat, etc etc etc. And she'll be fine when I'm standing outside, she'll play with Sobacca or be sniffing around or chewing on a stick or something....but as soon as I walk in the house she'll be heading over to her digging "spot" ---she always seems to dig in the exact same spot when we're there. And she's a very fast digger!
That would NEVER work with Minna -- she could care less about stepping in poop that's in her way in the yard. Although she did step in some a few weeks ago (apparently I was slacking on keeping the front yard clean :blush. And she wasn't too happy about having poop on her paw, so maybe it would work.Put a little of the dogs poo in the hole and cover it up. That will stop them there in that hole and then training.