I have been on QM2 eight times now and she is without question the most stable ship that I have been on. We had a Force 11 gale on a crossing this summer and the vast majority of passengers were out and about. In fact, a large number were sitting by the windows on Two Deck watching the waves crash against the windows.
I have done the run down to the Caribbean a number of times on QE2. Typically, the first day is sort of cold and grey. However, once the ship passes Cape Hatteras, the weather starts to warm up and become nice.
I was on QM2 going to the Caribbean in April. There was a storm heading back to NYC but that did not last long.
It should be noted, however, that any ship can move about. It is very much a personal thing how affected you will feel in response to the motion. I have met people who complained about the ship's motion when she (QE2) was still tied to the pier.
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I hope this is helpful.