large Gallstones are extremely difficult to dissolve via any method, and where there is a distinct risk of developing "Obstructive Jaundice". This is often accompanied by severe irritation of the skin ('pruritus') due to a buildup of bile in the blood. A very unpleasant condition with loss of appetite/digestion and severe loss of weight.
Surgery may be your only viable option in the short term, so a second opinion would be essential I would think.
Lifestyle changes post surgery, as in diet, would prevent the further development of stones, as their cause is often due to abnormal Liver secretions thru a faulty diet/lifestyle choices.