Air carrier Captain reported temporary loss of control due to wind shear during two landing attempts resulted in a diversion to a nearby airport.

Narrative

During arrival briefing; noticed moderate turbulence on the app and ATIS winds of 030@27G41. First Officer (FO) looked up gust factor crosswind and it showed 31kts which was within limits. We agreed to use flaps 3 to reduce impact of crosswind gust on aircraft stability and added 3kts to Vapp. I briefed a visual to 08L backed by the ILS and the wind-shear recovery maneuver. I also briefed the FO to not call Tower in the event of a go around until after we had finished the initial steps and climbing out so that I could be fully attentive to their directions. At 1;000' winds were calm and we were very stable with light winds at 500'. Somewhere between 300-400 feet the airspeed rapidly increased to about plus 20kts and I believe the FO called for the go around on our first attempt. We executed it as briefed and the FO stayed with me until climbing out and then notified Tower. FO did an outstanding job re-sequencing the box; getting the after take off checklist done; doing the descent checklist and briefing another visual approach for me. On second approach; I had the Autopilot and auto thrust on until 500' and again we hit the surge of airspeed under 400' and since idle wasn't going to fix it; I did another go around. We decided to attempt it one more time with increasing Vapp to 155kts to protect against a just as sudden airspeed decrease and have margin to prepare for the sudden increase by being more comfortable with going to idle to correct. I also asked the FO to get ATIS for ZZZ1 and agreed to use that as our divert. Things were happening fast because we were in a visual pattern keeping it close to the airport due to all the small plane traffic in the area. On the third attempt our plan worked better as I was able to anticipate the airspeed increase and deal with it. After shifting my aim point under 200' and about 100' I started to pick up a large drift to the right and the plane had an uncommanded angle of bank (AOB) roll to the right. FO called for the go around while I imputted large side stick to the left and went to TOGA. Fuel; wasn't a big concern but when we heard the gust at 50kts; we had had enough and agreed to divert to ZZZ1. Because of the traffic in the area; I elected not to hold overhead while I spoke with Dispatch and simply ACARS dispatch that we were diverting to ZZZ1. The FO did an amazing job handling all the calls; setting up the box and briefing for me at low attitude. Landing in ZZZ1was uneventful and welcomed!