Flight Instructor with student reported alternator failure and a return to departure airport.

Narrative

On an IFR departure out of ZZZ; everything was running well. We climbed via the ZZZZZ 3 departure to 3000 feet; then got radar vectors and steps up to 5000 feet. At 5000 feet; we were level when an Alt 1 caution CAS Message showed up. At this point; we (my student and I) clicked over to the engine page to see zero amps on alt 1. I then attempted to load the alternator using the AC with no change. I did this as sometimes Alt 1 doesn't take much load so it will show up as a failure; though it shouldn't while in flight. My student then cycled Alt 1 with no change. I then took controls from my student and instructed him to read the Alt 1 CAS checklist. This checklist asks us to verify the circuit breaker and then cycle the alt. We did this two more times. each time; the alt would come online for about 10 seconds. During this time; the amperage would wildly fluctuate between about 4 and 10 amps before falling to zero again. During this; I was instructed to climb to 7000 feet. Upon reaching 7000 feet; I informed ATC of the failure and asked to divert back to ZZZ. In a Cirrus; the Alt 1 is the critical alternator; however; you still have 30 minutes before anything fails and nothing critical will fail. ATC asked me if I wanted to declare and because I knew this fact; I declined. At this point; I was given a vector back toward ZZZ. My student was finishing the checklist by turning off systems on main bus 2 and shutting off the alternator. This disconnected the yaw damper. At this point; ATC asked for my approach request. I hadn't had a chance to look yet; so I asked for the RNAV XX. He asked which RNAV so I told him to standby. After looking; I asked for the RNAV Z as it was an LPV. Right about this time; we got a essential bus warning CAS (indicating it was no longer on ALT 1 voltage and completely normal) and an essential bus warning CAS message. After pulling up the engine page; we saw that the essential bus was now on bat 2 voltage of 24.2 V. This is not supposed to happen. The essential bus should be on alt 2 voltage minus one volt; making it 27.75 volts. I asked my student to pull up the electrical diagram of the cirrus to verify. Once we verified this; we knew something else was wrong. I looked up and saw that we still had 17 minutes indicated to the airport if we went direct. Since we were still in IMC and needed to do an approach; we would be running close to the 30 minute reserve on batteries. This meant we could potentially lose all avionics. Even though alt 2 was still showing that it was working; something was clearly wrong. At this point; I told ATC I was [requesting priority handling] and they vectors me straight toward final. At this point; I told my student to continue running checklists for the CAS messages and I would continue to fly to the ground as he had only flown in IMC a couple times. From this point; I made my best forward speed of about 160 KIAS and followed ATC vectors and altitude for the RNAV Z XX approach. No further faults were indicated; however; the essential bus voltage slowly dropped to 23.9V by the time we landed. After landing; we taxied in and were met by the fire crew to make sure all was OK. That was the end. We shut the aircraft down; put it away and informed the flight school of the failure before grounding the aircraft for maintenance.