Well, for starters it probably did happen at the sink but not in the way she described. That is probably where she got the idea to add it to her story. The problem with that brainstorm is that there was no evidence of blood that gushed out in the location she claimed. Just as there was not evidence that a bloody knife had dropped or been thrown onto the vinyl flooring. If she was telling the truth, the physical evidence should have backed up her claims. So the conclusion is that the knife was not thrown on the floor by a fleeing intruder and Darlie never leaned forward to pick it up and gushed blood on the floor.
Besides, she changed it by the time she got to court and said she first noticed she was cut when she saw herself in the mirror of the wine rack when she was on her way back to the family room to get Darin who was upstairs sleeping. If you look at the kitchen,that rings true too. But I doubt if either one happened at the times and for the reasons she gave.
To answer your first question, yes, people have discussed Darin trying to disarm her and some have suggested that he was the one who cut her throat. I don't think anyone has said they thought he attacked her for killing the children, though that is not bad. He didn't do enough damage though to think that is what really happened. If he had been that angry with her, surely she would have been a bit more cut up. Or beaten up. And if that is what happened, why not just fess up afterwards. It would have been justifiable, that is for sure.