Hello, Welcome to Just Answer and thanks for your question. Do you mean you have had your gallbladder removed and there is now a stone in the common bile duct?
Other than the prescription medication ursodiol there is no way to dissolve gallstones. When there is a stone in the duct after a cholecystectomy, then a sphincteroctomy (a surgery through the sphincter of Oddi with removal of the stone) is performed. It is also done with a laparoscope and is an outpatient procedure.
Yes, they enter into the abdomen with a small laparoscope. It takes incisions about 1/2 inch long to insert the instruments.
Nothing dissolves a gallstone except ursodiol.