He only went to her house because if he didn't, the press would say he refused to apologise.
Everyone I know vents under times of stress, either in the car, when they put the phone down, when they come in in the evening. Not really a big deal and I'm sure Cameron says much much worse.
What I found more telling was how badly he thought the encounter had gone. Most politicians would have considered it a success but he is obviously so used to being told he is useless with the general public that paranoia has set in (or vice versa).
As much as I have respect for him and think his treatment is unfair at best, it has reached the point where he is unsustainable. As PM you don't necessarily need the press behind you, but you certainly don't need them berating your every action all day every day.