Air Carrier Captain reported a communications breakdown between the flight crew and ground personnel regarding the selection of a suitable destination alternate airport. After further investigation it was determined the original alternate airport was qualified.

Narrative

This flight was planned to carry Class 1 HAZMAT [Explosives]. The final air mission briefing sheet was given to me to review. The briefing included the following statement about our alternate -- 'Alternate Airports: X airports should be given first priority. Any other approved company alternate may require additional approval.' Our alternate airport was given as ZZZ1 airport. I called my Dispatcher and asked if ZZZ1 was approved as an alternate airport; per this statement above. Dispatcher looked up the same note and said they would check and get back with me whether ZZZ1 was approved and appropriate. A few minutes later; Dispatcher called back and stated that system operations told her they did not know whether ZZZ1 had been pre-approved as an alternate for this flight. They could not find any documentation of that as the person that would have done it was gone and it would have been done earlier in the day.With this information; both the Dispatcher and myself agreed that it would be prudent to change the alternate airport to a military airfield. If we had to divert; there would be no way to get permission to land at ZZZ1. We jointly chose ZZZ2 as an appropriate alternate. We amended the flight plan and I added fuel to the airplane. A while later; I checked the ZZZ2 in Jeppesen. ZZZ2 has a curfew after XA:00 local time; after which the field is closed. I messaged my Dispatcher with that fact. After another few minutes; my Dispatcher called me on the phone again. This time; Dispatcher was noticeably upset. Dispatcher said someone from system operations had screamed at her that ZZZ1 was pre-approved and that she should have seen it before. Dispatcher was unable to continue her duties dispatching; so I told her to take a break and I would handle things from here on out. At that point; I called Chief Pilot and explained the situation. I was not convinced that ZZZ1 was approved as an alternate; nor that it was required to be pre-approved. No one had a concrete answer for me. The next day when we ultimately took the flight; our alternate was ZZZ2 and I accepted that flight plan with no questions.I don't normally inject my personal comments; however the behavior of personnel in system operations was unacceptable. The Dispatcher is a crew member. They cannot be intimidated and should be treated as any other part of the flight crew. Attitudes like that have no place in flight operations and I will not operate aircraft when any member of my crew is being harassed. I also will not tolerate 'pushing' the flight out when there is question on the legality of an alternate. Unless BOTH the Dispatcher and Pilot In-Command (PIC) agree on the decision being made; the flight should not operate.