I know of a marriage where both husband and wife desired children, but the marriage was fruitless. Yet after they were divorced and remarried both became parents. How can this be?

This proves that both parties were physically capable of having offspring. Their first marriage was barren because no incarnating ego was drawn towards it. There can be several reasons for this. Unless an incarnating ego is there and destined to be re-embodied through a particular couple the physical efforts of the latter will be fruitless. If physical factors were the only consideration to be taken into account there would be no reason for the first marriage to have been unfruitful while the subsequent ones produced children.