From your description, it does sound like the response of the Psychiatrist is inappropriate.
It is expected that a Pharmacist would flag any case in which a patient is getting two different benzodiazepines from two different doctors, but if this were to happen in your case, the usual next step is that when the Pharmacist communicates with the Psychiatrist, the Psychiatrist simply states that the use of Valium from your primary care physician was known, and that the treatment plan is to change to the Klonopin. And as long as you do not try to fill both prescriptions, there would typically no longer be an issue
So, it is still baffling why there is still an issue, and it reflects an issue more with the Psychiatrist than the Pharmacist.
At this point, though, it is probably not as simple as deciding to just continue care with your primary care physician as though nothing has changed, because the Pharmacist concerns needs to be addressed. If you do not want to continue with the Psychiatrist, it would be better to contact your primary care physician immediately, rather than waiting for your next scheduled appointment. You can communicate the sequence of events and the discussions with the Pharmacist and Psychiatrist, and your primary care physician can decide on the treatment plan including whether to continue the Valium or change to Klonopin under his/her prescription, and then he/she can communicate with the Pharmacist to address the concerns.
If you feel that you still need to see a Psychiatrist, but prefer to see a different Psychiatrist, it would be better to get resolution of the current issue before adding another doctor into the situation, so you can either wait until the investigation is complete or you can still use your primary care physician to address the current issue, as above, and then seek care with a second Psychiatrist.
If I can provide any additional information, please let me know.