One of the more remarkable stories along these lines involved the ill-fated annulment of the marriage of Joseph Kennedy II to Sheila Rauch Kennedy. In this case the Boston Diocese actually granted the annulment, but his non-Catholic wife successfully appealed the nullity ruling.
Wanna talk about Henry VIII and Catherine and the whole consanguinity thing...that didn't work out the way he wanted it to? But which had been used sucessfully by others before him.