Without defending his actions, it was something that was going to happen anyway, if he's that unstable towards his own Mother. It was only a matter of time before he got angry at someone and did something brutal.
Maybe only if you've got a long distance to travel, and can't afford a flight. Otherwise, try and group all your cities together, THEN get the train to a new area once you've visited all one area.
Personally, I'd be bored sitting on a train, knowing it was going miles away from somewhere I wanted to visit, just to get to somewhere else. You lose that spur of the moment thing, as you can't just get off a train and get hold of a car that easily.
Budget is the biggest factor. Once you know how much you're likely to have available, then you can work out some kind of itinerary. Hiring a car and staying in budget motels isn't such a bad idea. If you're not freaked out about sharing, have a look at couchsurfing.
Regarding places to visit. Just chose cities that you wish to go to for a specific reason. No point in spending a day driving, just to look at nothing special, just to say you were in (insert city).
RE: Cats
Cat, forgot to cat when they woke.