A TRACON Controller reported a GA pilot became disoriented in IMC and deviated off course when their attitude indicator failed. The GA Aircraft flew below the Minimum Vectoring Altitude and into a confliction with an aircraft on approach.

Narrative

Aircraft X requested the GNAV XX into ZZZ. Aircraft X was level at 3000 and I cleared them direct ZZZZZ; the initial approach fix for that approach. Aircraft Y was being vectored for the ILS ZULU RWY XX at ZZZ1. Aircraft Y was level at 1700 on a base turn. I then noticed Aircraft X changed direction without any notice and a low altitude alert started to go off. I immediately gave a low altitude alert to Aircraft X and saw his altitude at 1100ft. I told him to climb to 1600 immediately. This is when Aircraft X advised me that he was disoriented. Once they were level at 1600 I turned him on a 270 heading away from Aircraft Y. Because of the sudden descent; I lost lateral separation. I then turned Aircraft Y on a 090 heading to also turn him away from Aircraft X. Aircraft X asked for higher and a vector towards ZZZZZ so I gave him 3000 and a 145 heading because I had Aircraft Z at 4000 being vectored for the ILS ZULU RWY XX at ZZZ1. Aircraft X then advised me that their 'attitude indicator' in their plane wasn't working. I offered no gyro vectors and they accepted. I began to give no gyro vectors but they were not able to turn in the proper directions. Aircraft X then asked to climb again. Because of Aircraft Z; I said unable due to traffic. He then began to climb. I turned Aircraft Z on a 060 heading to turn away from Aircraft X then gave Aircraft X altitude their discretion because I was unsure what altitude they needed. Once they began to climb I then asked what altitude they needed and they said 4000. I then told Aircraft X to maintain 4000. At this point Aircraft X was no longer in conflict with any other aircraft and advised me that they were above the cloud tops. Per their request; I began trying to vector them again for the GNAV XX into ZZZ. They still could not hold a heading. I tried putting them direct fixes for the approach and that did not work either. Aircraft X let me know that he was shaken up by all this and really just wanted to get on the ground. I asked him if he would like to try to go to another airport that had better weather and he said yes. I weather requested multiple airports and found that ZZZ2 was the closest with the best weather. Aircraft X then began to divert to ZZZ2. Prior to Aircraft X getting to ZZZ2; the east controller asked one of their aircraft to check out ZZZ2's weather to make sure it was good enough for Aircraft X. That aircraft reported VFR conditions at 3000 southwest of the airport. I then vectored Aircraft X to that location. Once Aircraft X was able to see the ground; they asked for a special VFR clearance so they could descend below the clouds and try to get to ZZZ again. I gave them the most recent base report of 900ft and advised them that might not be a good idea. Aircraft X then decided to cancel IFR and proceed VFR to ZZZ2. The watch supervisor did call the ZZZ2 airfield management and advised them of the situation and requested emergency vehicles to be on standby just in case. They were able to land at ZZZ2 safely.