Hi,
I'm not sure how you do this with two dogs & unclear status, but do you have toys for outside? My two have a lot of treats toys but the non-dominant one knows she has to just wait & watch for any left overs. Doesn't sound fair to us but it is only "entertainment" food in the treats dispensers and the smaller dog interacts following around & watching. This might cause fighting so get more advice from people that know more than me, but alternative sources of entertainment while you ar egone may limit the digging.