If you are diverting to the alternate you're going to use destination minimums because that's where you're going.
Gotta remember too, once the declaration is made to divert, you're not using alternate minimums anymore. Few folks at my former shop had trouble understanding this.
The crew will use destination minimums for the approach, but so long as the airport is listed as the alternate, it must remain above alternate minimums.
121.625:
Except as provided in §121.624 for ETOPS Alternate Airports, no person may list an airport as an alternate in the dispatch or flight release unless the appropriate weather reports or forecasts, or any combination thereof, indicate that the weather conditions will be at or above the alternate weather minima specified in the certificate holder's operations specifications for that airport when the flight arrives.
121.631(b):
No person may allow a flight to continue to an airport to which it has been dispatched or released unless the weather conditions at an alternate airport that was specified in the dispatch or flight release are forecast to be at or above the alternate minimums specified in the operations specifications for that airport at the time the aircraft would arrive at the alternate airport. However, the dispatch or flight release may be amended en route to include any alternate airport that is within the fuel range of the aircraft as specified in §§121.639 through 121.647.
Legal interpretations don't provide much guidance on the topic as they simply point to "if weather at the alternate falls below alternate minimums for the ETA at that airport, the alternate may be amended IAW 12.631(b)."
The 8900.1 doesn't go much further than that. Review 8900.1 Vol. 3 Ch. 25 Sec. 3 3-1977. Specifically B. Alternate Weather Requirements While En Route. This section stipulates that a flight may not continue to
destination while weather at the alternate is below C055 mins.
Additionally, 8900.1 Vol. 3 Ch. 25 Sec. 4 3-1988(F) indicates that weather at the alternate must be at or above C055 mins at the ETA to the alternate.
There is no provision allowing for weather at the alternate to fall below alternate minimums simply because the flight is diverting to the alternate.
An airport is not a destination or alternate based on where it is proceeding to. Destination and Alternate are designations on a flight release that have implications for fuel planning. Listing an alternate is authorization for a flight to proceed to and land at that airport without an amendment, as it is part of the original plan.
It all boils down to how the diversion is processed.
If you are diverting to the alternate without recalculating anything, it is still your alternate, and must be above alternate minimums for the purposes of the flight release.
If you are diverting to the alternate, but you have recalculated to show the alternate as "destination", then you have changed destination and will need to list a new alternate if that new destination is below 1-2-3.