I have he same issue, but mine is they respond as if they don't have a shovel when all 4 have one in inventory.
I believe this to be a save game bug.
I progressed to go to Myrna(sp) tombstone and a mound popped up there, same issue, older toons could not dig. Didn't have the new toon created yet.
I created a new toon in camp and when I use him to dig, he works fine, the other 3 do not.
I haven't gone back to an older save yet to attemp a fix because dirt mounds are so random(I presume), makes it hard to test.