Random aggressiveness to my other dog

I desperately need some help. I have a one year old Basenji mix and a five year old retriever mix. The five year old is pretty passive. The one year old has had medical problems (congestion, coughing) for her entire life and the vets have said it will never go away but could be controlled. She seems to be feeling better but some days are better than others. The problem is she randomly goes off and snaps at our other dog. They could be playing for 15 minutes and all is fine. Five minutes later, she snaps and wants to attack him. She has also snapped at my wife and bitten her a couple times. We are working with a professional trainer but fear training won't be enough as we can't determine the trigger that sets her off. I don't want to give her up but for my wife and my other dog's sake, I may have to. Please give any suggestions on how to solve this problem.

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