This is where I think the source of Tywin's power lies. Everyone else. Tywin destroying the two rebel houses Reyne and some other foolish family wasn't about vengeance; it was about sending a message. Tywin-propaganda is all over the Seven Kingdoms, and the Lannister theme song is sung as often as The Bear and the Mainden Fair. There are many sayings about House Lannister (Tywin shits gold; a Lannister always pays his debts), as the smallfolk and the nobility are wont of reminding one another. As readers we can judge his battle commanding skills, and those don't seem to be great at all. His fleet was burnt in the Greyjoy rebellion, and he was crushed by a 16-year-old boy about 5 times in battle. The only significant victories he had were the Battle of Blackwater (and that would have failed if not for Tyrion's wildfire nuke) and the Sack of King's Landing, by use of treachery. Other than being rich, there seems to have been no factor to his reputation other than how he crushed the rebels (which was easy enough with the rest of his bannermen at his back), and the propaganda that arose from that. Anyway, this propaganda is so strong even Robert Baratheon fears slighting him. Everyone fears the mighty Tywin. He pretends to be a completely cold man, to retain that reputation, but through Cersei we know this is only a mask. Everyone everywhere needs to do exactly as he says. And he's always been a cunt.