Hi there --
There are a number of possible causes of this, and the one which most closely resembles what you describe would be pertussis (whooping
cough), which is well known to cause deep
coughing which triggers
vomiting. However, it also could be due to gastroesophageal reflux (
GERD), or a number of other things. She needs to be worked up for this problem, as there's nothing good or even very tolerable about this sort of problem. If it should turn out to be pertussis it can be treated symptomatically until it resolves on its own; if it is due to
GERD, this can be treated specifically and the problem relieved. If it is anything else there should be some means of management. First it needs to be diagnosed, however.
I hope this is helpful. Good luck to you both.