The first step is to find the source of her mucus. It could be her nose or sinuses. If her cough producing yellow mucus is chronic, this could be the result of a chronic lung disease. She could have what is called bronchiectasis, with or without cystic fibrosis. Once again if this has been going on for several months or more, she should see a pulmonary specialist.
I too have a similar feeling in my throat. I do not cough mucas though. I have a lot of post nasal drip as well as acid reflux that seems to be bothering my voice box and wind pipe. The sensation in my throat, where you described, when really bad makes me feel like I want to cough. Maybe she wants to check into acid reflux, the coughing is a sign of acid reflux . . . I can not feel an acid reflux symptoms. it is called "silent" . .. and possibly allergies?