My daughter has been vomiting two three times a day along with loose stool. However she is feeling good and is pretty happy. She does complain that she has something bitter in her throat and usually vomits after cauphing?

Tricky. cannot say in your particular case, but generally, the problem would be dehydration. More of an issue if not taking oral fluid, if vomiting and diarrhea, if below 2 yr old. Also abdominal PAIN, fever, distress and many other features indicate a potentially more serious condition.
Post-tussive emesis. It's normal to throw up if you cough hard enough. She may have stomach flu w/diarrhea. As long as she's happy & can keep fluids down, just monitor closely. Many OTC cough suppressants available. If persists or worsens or can't drink, then needs to be evaluated. .