CL65 Captain reported they a return to the departure airport due to pressurization issues and an inoperative air conditioning pack.

Narrative

While operating the flight ZZZ - ZZZ1; we deferred the number two pack during the taxi and departed with single pack operations. Through 10;000 ft. I noticed the cabin temperature was high. I asked the FO (First Officer) to adjust the temperature. As soon as the temperature was adjusted there was a lost in airflow sound and pop noise. The FO selected the ECS (Environmental Control System) page showing the left pack failed. We asked ATC to stop our climb at 15;000 ft. to work on the issue. I called for QRH for non-message both packs inoperative. We determined that the non-message checklist for Pressurization - Unpressurized Flight Procedure" was appropriate. While looking at this checklist and the ECS page the number one pack started operating. We noted the first checklist item would be a descent to 10;000 ft. and decided to hold the checklist because the pack was operating. Then the pack failed again. We requested a descent to 10;000 ft. with ATC. At 10;000 ft. we proceeded with the QRH.The checklist option for one pack operating stated EMER Depress confirm and open. When we selected the button; the cabin climbed to 8000 ft and CABIN PRESS amber message displayed. My ears were severely uncomfortable and the FO was in extreme discomfort breathing. I decided to abandon the QRH procedure and reversed the EMER DEPRESS selection. The pack was still operational and the pressurization returned to normal comfort level. We advised air traffic control and ATC gave us a decent to 6000 ft immediately following this event; the flight attendants called us to ask what happened. I advised them we were working on a pressurization issue. One FA (Flight Attendant) said the passenger were having discomfort and were anxious. I said I would make an announcement. I made a PA announcement assuring the passengers that we we were working on the issue and we would update them shortly about diversion details. We notified dispatch and they returned with ZZZ for the diversion. Once we advised ATC of our decision to return to ZZZ; they issued a clearance direct to the airport. We began flight planning the return to the airport. I informed the flight attendants of their briefing items and advised the passengers we were returning to ZZZ. While I was doing the brief items the FO was programming our return to ZZZ. We setup for the approach; briefed and performed the descent checklist. We monitored the pack operation throughout and opted not to adjust the temperature. The pack continued to operate throughout level flight and descent on the approach. We arrived at ZZZ without further issues with the pack. After exiting the runway; we taxied to gate. We did not have crew or passenger injuries during this event. The passenger all deplaned under their own effort.The airplane had a history of maintenance deferring the number two pack. Operating it in this state in a hot environment may have contributed to the increased demand on the remaining pack causing the intermittent failures. Removing the airplane from the hot environment during single pack operation may be a solution."