I think that she "stuck with him" because she had no where else to go. Where does the woman who almost brought down a government and who did bring down a Duke and King go, if she leaves the man?
Even if she decided that she hated David after a few years, I don't think that divorce (yet again) would have been an option. Divorce was what got her into trouble in the first place. Not one but two! And remember the time period that we are dealing with. In the 1930s divorce was not seen as "good behavior" or as moral. Much different from today.
To go for a third from the man who loved her so much that he let down his country his government and his family for her would have been just too much!
The person whom I always thought the most interesting in all of this was Queen Mary. She had helped to speed up her husband's death and expected her son to follow suitably along and take up the reins (or reigns). But he didn't! Can you imagine what Queen Mary must have gone through?
I haven't seen the movie yet, but I hope to find a theater around here that is showing it. I was surprised to find it on the awards list. It doesn't fit the usual best movies genre.