If possible try placing chicken wire under the dirt. if she digs and hits the chicken wire he won't want to continue to dig there. My parents had the same problem and that's what they tried and it actually stopped them from digging completely.
I'm really looking to get a goat, but I'm not sure about getting two since I know they should be with at least 1 friend. I have a red heeler, and I'm wondering if it's possible for my dog to fill the space for a friend rather than a second goat although my dog would still spend time inside.