Eva never actually says that she wants a divorce from Adrian. But after she discovers that he's been cheating on her with Betsy D'Amido, that's certainly the direction in which the Smiths' marriage is headed. Seven years since their honeymoon, it now seems that it's all over for the Smiths, and all because Adrian lost his head over some pretty young lady who rashly proclaimed her love for him when they met for the first time.
But by a remarkable set of circumstances, the Smiths' marriage lives to fight another day. This is largely for two reasons. First of all, Adrian bravely ventures out on to the deck in the middle of a vicious storm to save Eva. One doesn't know for sure, but one gets the impression that Eva was rather impressed by this selfless, heroic gesture.
Secondly, and perhaps more importantly, Adrian has agreed to buy Eva an expensive set of pearls. Taken together, these actions convince Eva that perhaps her marriage might be saved after all, and that she's better off sticking with Adrian. That doesn't mean she can ever forget the unpleasant incidents aboard ship leading up to the storm. But she can at least move on from that terrible period when it seemed that her seven-year marriage to Adrian was about to come crashing to an end.