ERJ 145 Captain reported a fumes event during cruise and diverted to another airport.

Narrative

Operating ZZZ - ZZZ1; I was operating upgrade OE (Operating Experience) from the right seat; my student was in the left seat. Before the flight; we MEL'd Pack 2 due to it not putting out any airflow. We reached our cruising altitude of 24;000. A few minutes later; after completion of the Cruise Checklist; my student and I noticed a strong burning smell and immediately decided to divert. I requested he run the Smoke/Fire/Fumes QRH and I took the radios. I [requested priority handling] with ZZZ Center and requested immediate vectors to ZZZ2. The smell subsided after about 3 minutes; after my student turned off the gasper and recirculation fans. Our FA informed us he also smelled the smoke towards the flight deck but not in the cabin. We let Dispatch know of the [priority handling] and we alerted our passengers as well. We landed and continued to the gate without further incident for the flight. Afterwards; I spoke with Chief Pilot (CP) and Dispatch Supervisor to debrief and come up with a new plan. CP asked if we were fit for duty; after discussing with my crew we decided we were okay for now; but not if there was a large delay. I relayed this to the CP and he said he understood. Dispatch then let us know the plan was to MEL both packs and go unpressurized at 10;000 and no AC. I declined the aircraft due to the rising temperature inside the cabin and flight deck and told them I needed both packs operational to take the aircraft. They then let us know that we would have to wait for a plane from ZZZ3 due to arrive at XA:30. By this point an hour had passed and I relayed this to the crew. Adrenaline had worn off and we were all very tired; so I called the CP back and let him know we were no longer fit for duty. He said that because I initially said we were okay I can't go back on that and that it's a fatigue call. I let Scheduling know; and they gave us a new schedule to sit in ZZZ2 until a new crew arrived and we would deadhead to ZZZ1. We all agreed this was out of line after the day we had; and I called the CP again to request that we just go to the hotel in ZZZ2 after all this. He told me I should've called unfit for duty right away and that it's turned into a [expletive] show" and was very upset about the request I made. He ended up telling me there was "nothing we can do" and that we had to sit for 5 hours total in ZZZ2. Scheduling ended up deadheading a crew from ZZZ; we deadheaded on their flight; we had a minimum rest overnight in ZZZ1; and then the other crew ended up deadheading back to ZZZ; so we essentially had two crews for one round trip.Root cause was Pack 1 - ACM (Air Cycle Machine) unit according to Maintenance - failing in flight and causing a burning smell. Maintenance needs to start fixing packs more rather than letting them run on one pack where they can overload and fail. Operations gave us no help after the fact either; between trying to get us to go unpressurized and then the unfit for duty situation. Crews should be able to call unfit for duty even if it's been an hour afterwards when adrenaline has worn off. Operations and the CP let us down after we successfully diverted during a [priority handling] situation."