Dogs will be dogs. However, they would not be digging their way into your yard, if a) there is something they want to get away from or b) there is something they want in your yard.
Spend the money to put cement or concrete blocks below the fence as suggested above. Dealing with some neighbours is like dealing with squirrels, you just cannot win the battle. So why cause yourself more stress.
No one ever promised that like would be fair.