Air Carrier Captain reported an unpleasant encounter with an approach controller while dealing with a malfunction of the aircraft's landing gear. The gear indicating lights showed not down and locked. The crew was running the QRH when the final TRACON controller was telling the Captain to maintain a visual with another aircraft; telling the crew to maintain a certain speed; and asking questions about speed. The Captain feels the controller did not help the high workload situation.

Narrative

While landing Runway XX passing through 2000 ft. the FO (pilot flying) called for the gear. The gear would not come down. We executed a non eventful discontinued approach. We climbed to 3000ft runway heading. Tower switched us to approach. They gave us an extended box pattern for runway XXC. We tried to contact company (unsuccessfully) and set up for XXC ILS and program the FMC. We transferred controls and ran the QRH (quick reference handbook) for manually extended the gear. We ran our checklist (all the while trying to reach company). While we running the checklist we switched to final approach control (this will be discussed below). We turned final and landed and rolled out to the end of XXc uneventfully. We shut down and waited for a tug back to company property. The Tower and first approach controller were extremely helpful and professional. The final approach controller I have some issues with.As we were heading east back towards the arrival pattern; we were 3000 ft and she called traffic; a 76 southbound at 4000 ft. We acknowledged the contact; she then told us; a priority aircraft to maintain visible separation. The workload was rather high at this point and adding 'maintain visible separation' seemed a bit unnecessary. When we turned final and called the field; she cleared us for the visual. Then she came back and told us to maintain 170 kts to a 5 mile final. I took the radio call and explained we're a priority aircraft and we're unable; she then demanded to know what speed we were going to fly. As a priority aircraft; running checklist; multiple radios; and flying; it seemed like the final controller did not give us the proper priority. Captain's Reaction to the event: Landing gear malfunction: Improper handling of a priority aircraft by final approach control.