I'm sorry to hear of this with Daisey. Considering her history of heart disease, it's reasonable to assume that her distended abdomen is effusive; in other words, contains free fluid indicating right-sided heart failure. This is easy to confirm by X-raying or ultrasounding her abdomen. To clairify what such fluid represents, a sample can be aspirated from her abdomen and sent to our pathologist to examine its cellularity and physical qualities. There are other causes of an effusion - the inflammation associated with infection and malignancy, bleeding into her abdominal cavity (unlikely if present for a year), and a lack of albumin (a small protein) in her bloodstream. When a poorly functioning liver can't produce enough albumin or albumin is lost through damaged kidneys or bowel, an abdominal effusion can arise.
Gastrointestinal disorders, dental and oral disease, central nervous system disturbances such as brain tumors or hydrocephalus, electrolyte imbalances, metabolic diseases, and toxins such as lead can induce her licking, sucking, chewing, and picas (ingestion of inanimate objects), licking of owners, and air licking.
Daisey's vet will want to perform a thorough physical exam including diagnostics in the form of blood and urine tests. If you think that Daisey is eating and drinking more than she should, her vet might consider Cushing's disease which also can cause a "pot bellied" appearance. That pot belly wouldn't be expected to improve, however, as you've noted. Please respond with further questions or concerns if you wish.