Air carrier First Officer reported temporary loss of control on short final on two attempts at landing due to wind shear and turbulence.

Narrative

I was scheduled to operate XXXXXXX which consisted of a ZZZ turn from ZZZ1 with a report time of XD:10. Upon reviewing the flight plan; nothing seemed out of the ordinary. The weather looked fine and there was no alternate or exemption listed. When we checked in with ZZZ Approach; we were informed that there was Aircraft Y in front of us that had attempted the approach twice and had gone around for windshear both times and was now diverting. I was the PF and we encountered very serious windshear below 500'; the airplane was extremely difficult to control (often full deflection of the sidestick) and we had an instantaneous gain of about 20-25 kts. and oversped the flaps which included the master warning light going off. A go around was conducted and as a crew we decided the Captain would attempt the second approach and that it would be flown with flaps 3. We attempted the approach again and got windshear below 100' and had a very sudden and steep wing drop. Another go around was conducted. We were nearly out of extra gas (less than 10 minutes of extra time) and after coordinating with Dispatch we conducted an unplanned diversion to ZZZ2. ZZZ1 Approach began to give us delay vectors and we were left with no option but to declare minimum fuel. An uneventful landing was performed into XXL in ZZZ2 and we landed with 46 minutes of fuel on board. Once we got to the gate in ZZZ2; my Captain and I decided that neither of us were comfortable going back into ZZZ that day. We had both been up since around XA:15 and we assessed the threat of continued windshear plus the weather system moving into the area that would leave the runway wet and/or contaminated. My Captain informed the Dispatcher we did not want to go back into ZZZ and he began coordinating with scheduling. We received a schedule change that had us double deadheading ZZZ2-ZZZ-ZZZ1 and they had reassigned another crew to cover the flying. After some time passed; my Captain received a very disturbing phone call from the chief pilot. He left the cockpit to take the phone call and when he came back he looked entirely defeated. He informed me that the chief pilot told him that there were no conditions forecasted at ZZZ that were outside the limits of the aircraft and that we were being told to go attempt it again. This was confusing to us considering there weren't conditions outside of the aircraft limits the first attempt either; yet we were left with an extremely stressful situation encountering very significant windshear on both attempts. Our flight attendants had even informed us that they had six passengers throw up throughout the approaches due to the turbulence. My Captain had very firmly told the chief pilot that we had been up since before XB:00 and that we had decided as a crew to not go back. The chief pilot told my Captain that we should mitigate our potential fatigue with caffeine and that If your FO becomes tired then you can just take the leg and let him be the PM." It was apparent that if they had stuck with their original decision of recrewing the flight; a substantial delay would take place; probably due to the weather around the system and lack of available crews. The chief pilot's attitude and directions completely undermined the Captains authority and seemed largely based on the fact that we were their only and best option to get the completion factor . It was unbelievably concerning that the attitude of the chief pilot was to just 'go get it done'. We were left with two options. Either succumb to the orders of the chief pilot or call out fatigued. We assessed our fitness for duty and determined that at that current point in time we were not fatigued so we went; while continuing to caffeinated per for chief pilot's official recommendation. The winds had now totally flipped in ZZZ so I performed the ILS XX which was required to be hand flown. We broke out 1;000' and an uneventful landing was conducted. The turn in ZZZ was slow and when we finally took off for ZZZ1; we were 90 minutes prior to our CCO (Critical Crew Off-time) time expiring. By the time it was all said and done; we arrived back at our cars nearly five hours late. It was an extremely stressful day including two windshear events; two go arounds; an unplanned diversion; declaring min fuel and nearly 12 hours TAFB (time away from base). My sleep the night after was entirely unproductive and restless probably due to caffeinated so late in the day and from the days events. When I woke up at XC:30 the next day for another turn I was completely fatigued; irritable; and exhausted. I decided that I was not fit for duty to continue with that days work."