GA pilot reported during landing lost control of aircraft while taxiing slowly; they exited the runway into the grass.

Narrative

We were transferred from Tampa approach to Sarasota Tower. They put us on a long final after several airliners for runway 14 our final was approximately 10 miles long. The wind was called at 12 kts gusting to 18 kts the tower asked us to keep our speed at 120 kts due to traffic in front of us once that traffic slowed and I saw they were on the runway. I started configuring for landing with flaps and insured we were completely configured for landing. I noticed there were three airliners waiting to depart runway 14 as we crossed the numbers for landing; I got slow and instead of doing a wheel landing I attempted a three-point landing and was quite slow. The strong cross wind was a little overwhelming from the right and I could not stop the subsequent push to the right as I slowed the aircraft. We slowly exited the runway as I was holding the brakes entered the grass on the side of the runway and made a quick 180 back onto the runway between Alpha three came back onto the runway and then exited at Alpha three. I should've stopped at the throat of Alpha three and Alpha; but I continued to taxi right onto taxiway Alpha as the tower told me to stop. The tower called for the trucks to come and meet the aircraft. I explained to them that we were fine. There was no damage they insisted we stop and wait and so we did. The tower transferred us to ground. We were then cleared to the ramp with the trucks and the operations people following us where we then parked. The trucks and the operations folks inspected the aircraft and determined that we indeed were OK and there was no damage. I did not have my certificates with me although my certificates and my medical are current. My passenger; who is also pilot did have her certificate and her medical with her; did show her certificates and medical to the operations person; and that there are controls in the front and back of the aircraft. We received a phone call shortly after to verify that everybody was OK and that the aircraft was not damaged. I also relayed to them my certificate number; and my name and address. We departed Sarasota to return home of about 30 minutes later.