I shared this original theory with a friend, and she liked it, but thought maybe rather than Juliet being David's mother, she would be some sort of OB/GYN specialist that is called in on the case because of Sun having been shot in her pregnant belly. I like that, too, so I'm just throwing it out there...
Of course, there's nothing to preclude her being both David's mom and the OB/GYN specialist that's called in for Sun...