Happy Elsa! All this sounds totally normal, but some of it should be addressed - like teaching not to paw at you to the point that it's painful. This is why some people don't like the "Shake" command, lol.
One thing I'd be doing is removing the collars, because she'll get her teeth caught in Sigmund's. This is a horrifying experience, trust me on that! And maybe curb some of the really wild play, so your dog isn't overwhelmed by her.
Can you dedicate a specific spot for digging? That's what I did for my pup, since he liked digging so much and my yard is large enough that a big hole behind the garden isn't an issue, lol.
It sounds like she just had a good time with her previous owners: mouthing, pawing, etc. and she'll need to learn some manners with your family. Training classes are always helpful. Good luck!