I do hope your mother's doctor elaborated on how to take care what she eats? Normally, people without a gallbladder are instructed not too much fat at a time in a meal. People with an inflamed liver are usually recommended to make changes to there diet.
The gallbladder holds concentrated bile when it is removed the bile isn't stored any more. Because the liver continues to make bile it leaks into the duodenum via the common bile duct.
People who have a gallbladder have the question; how does the Liver Flush itself when bile is available in the gallbladder? The answer is, because fatty acidic food leaving the stomach signals both the gallbladder and the liver to produce bile. The volume of bile from the liver is swelled by bicarbonated fluid produce by cells that line the liver ducts. Because of the nature and quantity of the flush potion this produces a powerful flush.