I am still hashing out the backstory of the Reynes, Tarbecks, and Lannisters, so nothing is fixed in concrete... but Tywin was not actually lord when he dealt with the Reynes (of Castamere) and the Tarbecks (of Tarbeck Hall). His father was still alive. Lord Tytos was an altogether different character, amiable but ineffectual, and he allowed himself to be pushed around a good deal, by a number of people.. including Lord Walder Frey (ever wonder how Genna came to marry so poorly?) and the Red Lion of Castamere, the richest and most powerful Lannister bannerman, and a formidable soldier/warrior in his own right...
Well, like I said, I'm still fine tuning it in my head. Not sure how much of it will make it into the books in any case...