Well, general rule of thumb is that all doctors should be accounted for and know what you are taking in my opinion. I agree that in the field of mental health and physical health, there are specialists in all areas. For example I have two psychiatrists, one a specialist in ADHD another in addiction. They both know the medication that I take (or should do) and have no objection to either, as the medicine does not interact (I'm supposed to be on dexedrine, subutex and diazepam).
It's generally a red light if the doctors don't know what meds you're taking from other places. It's not doctor shopping, but it is in a way. You're going to another doc with the intention of obtaining in this case xanax, as you know you cannot get it from your first doc. However, if you think he is not treating you properly and see another doctor who OK's the xanax and Prozac, why can't he prescribe both?
It's a fine line you're treading on really.