Hepatic lipidosis (fatty liver) is a strange disorder of cats. Any cat that becomes anorectic is a candidate. Treatment is supportive care and feeding, by surgically implanted feeding tube if necessary. The gagging may be a result of a feeding tube, esophageal reflux, nausea, laryngeal irritation, secondary infection such as yeast, etc., tracheal inflammation secondary to aspiration, and my list could go on.
The kitten's ear mites need to be treated, but I can't make a direct connection to the adult cat's coughing/retching.
If your adult cat is eating well, then this problem should resolve over the next month. Sorry that I can't be more specific, but too many things can cause the symptoms you describe.
Dr. Van Lienden
Dr. Raymond Van Lienden DVM
The Animal Clinic of Clifton
12702 Chapel Road, Clifton
Virginia, U.S.A. 20124