Air carrier Captain reported severe turbulence during landing which resulted in a missed approach. During the initial climb the flight experienced a windshear event; the flight crew executed the escape maneuver and continued to the alternate airport.

Narrative

Flight from ZZZ to ZZZ1; our crew was aware that there would be a potential for moderate turbulence along our route and some thunderstorms near the vicinity of the airport. Our passengers and crew were advised of the potential for weather; so we requested they prepare for landing and be seated early. We safely navigated around the weather and into the approach area for ZZZ1; where it was VMC. While being vectored for the ILS XY; we were advised of a wind shear report for Runway XX. I made the decision to continue; as there were no reports for Runway XX. We were stable at 1000 ft. AGL; but our descent was subsequently arrested and was followed by a rapid descent and airspeed loss. We got the wind shear warning and I advanced the thrust to max simultaneously and began the escape maneuver. I focused on my pitch and airspeed while my FO (First Officer) called out 'descending/climbing'. While attempting to maintain a steady attitude; our flight controls lost authority. My inputs were not effective momentarily. We heard ATC calling us but were unable to respond or comply; as we were focused on climbing out of the windshear safely. When we finally regained control authority and finally gained enough altitude to advise ATC that we needed higher; they were accommodating and continuously offered us higher altitudes in order to escape. We continued the climb to escape the severe turbulence. Around 16;000 ft; the turbulence began to subside. We leveled off at 18;000 ft. and were given approval from ATC to deviate for the line of thunderstorms ahead. We turned right to deviate and advised ATC that we'd be diverting to ZZZ2. We cleared the weather and followed all company procedures for the diversion; to include all required communications. We landed safely in ZZZ2. There were no reported injuries. My FO and I agreed that the event satisfied our criteria to write the plane up for severe turbulence; and we did so upon reaching our gate safely and performing the post-flight inspection.The cause was wind shear/severe turbulence escape.We did what was necessary for safety of flight. We landed safely with no injuries.