I've imagined that the succession would be the way you've put it.
You are probably right about remarrying. William must have felt that the succession was safe with his nephew.
But then if Iím not mistaken, the little Duke of Gloucester was always ill and I mean, as a king William should see that, and of course take action! Or perhaps he didnít care? :-?
I don't think the Duke of Gloucester was always ill - he had hydrocephalus, which meant his head was slightly enlarged and he had problems with balance, but most of the time he was alright. His death came as a surprise, it's only in retrospect that it looks as if it was inevitable. Also Anne was still capable of childbearing - she was 36 when she ascended the throne, though it admittedly looked less likely year by year.
William was not really a "ladies man". I doubt if he would have wanted a wife for anything other than having an heir.