I always assumed the timeline was that Anakin knocks up Padme (lucky bastard), he turns to the darkside of the force while she goes into hiding, she gives birth and he never knows, then she dies. So it wouldn't be her death driving him over the edge. Because if he knew about her death and wasn't pushed over already then the likelihood would be that he knew about the twins as well because he would have to be there to know about her death and she would've had to give birth to them before she dies, right?