If the digging is taking place at night, then I doubt that they are squirrels. They (squirrels) are not nocturnal. Possibly some other type of rodent? Raccoon, Armadillo,rats, field mice? Cats?
Not sure what critters may be in your 'neck of the woods'. You could try sprinkling cayenne pepper around the plants on the soil. Do you mulch? I've found that even mulching my container plants has helped to keep critters out. I'm sure that there are products available to deter 'wildlife'.You might want to check with a Nursery or Hardware store that carry such things.