Citation Captain reported experiencing continuous moderate turbulence and wind gusts on approach resulting in the aircraft rolling and the flight crew going around. The flight crew diverted to another airport where they landed safely.

Narrative

On approach to ZZZ we were experiencing continuous moderate turbulence due to high winds. We were following an airline. LLWS in effect for the whole area. Inside the FAF the Tower advised gusts to 47kts. It was only 10degrees off the runway. I don't recall the exact winds. I continued the approach because I could see the airline made a landing. After the 500 stable call the plane banked hard left. I used full right aileron and the plane kept slowly rolling. The yaw damper was still on so in the moment I was trying to use rudder to no avail. In 2 or 3 seconds we went back wings level and controllable. I looked down and we had lost 20kts. I announced go around and we commenced the go around. I elected to go to ZZZ1 based on my familiarity with ZZZ1 when I was at the airlines. Over water approaches are less turbulent and winds were favorable. Landed uneventfully Suggestions:Turn off yaw damper. Also brief missed approach callouts. We were caught unprepared. The missed went fine; we were never in danger; but it could've been cleaner though. I also wish I declared severe turbulence to warn other pilots. We did not declare it but I did write up the plane for it. Huge mistake on my part.