I'm Dr. Brian and I will do my best to answer your questions.
The problem with Dakota is called jaundice or icteric. The yellow color is due to bilirubin building up in her tissue. This is due to her underlying liver problem. Unfortunately blood work can only tell us its a liver problem and not what exactly is wrong with the liver. The only way to get a 100% accurate diagnosis is with a liver biopsy. This can be done with a needle during an ultrasound or with exploratory surgery. The ultrasound may be able to really narrow down the possible problems by showing shape, size, abnormalities such as tumors or abscesses. Many of the typical cat liver diseases have typical appearances on ultrasound that may better steer your vets tentative diagnosis and your cat's treatment plan. Some of the most common liver problems in cats are hepatic lipidosis (usually found in very obese cats that stop eating), cholangiohepatitis (what I suspect your cat has), and pancreatitis which can also be evaluated by ultrasound. Regardless, the treatment often involves much the same initial treatment. These may include IV fluids, antibiotics, special food and liver support drugs. One of the mainstays of this type of problem is a feeding tube so that much of the feeding and treatment can be done at home. One tube is called an esophagostomy tube and is easily placed in the neck and cats tolerate it very well. The other type is a gatrostomy tube and is much more involved in placing and is directly placed through the wall into the stomach. Your vet is truly not milking you but trying to get information on a very serious case. If no treatment is done most of the cats will die of starvation as they refuse to eat.