Brake and Battery lights on at the same time???

What is your question?

I have a 2009 Nissan Murano LE. A few weeks ago my Brake and Battery lights kept coming on and off together. Upon research, it seems it coulf be my alternator, or serpentine belt or something with the electrical system. I took it in to a NTB location and they did a diagnostic on my electrical system which checks battery, alternator, etc. and everything checked out fine. However, fast forward a couple of weeks, I am driving and both the lights are still coming and off but this time I had my A/C on and the lights were more steady and the car cut off. I turned everything off and restarted the car successfully but I am keeping my A/C off now. Also, The brake and battery lights go off at higher RPMs but come back on lower RPMs. My question is, what should I have the auto shop check this time OR should I just have them replace the alternator??