Given how powerful and dynastically smart the Tyrells and the Lannisters (or at least Tywin) are why does there seem to be so little connection in recent history pre-ACOK. It seems the two could have formed a pretty strong, for lack of a better name, “western ambition” plot. Is there any reason for this?

Because they’re historical rivals. If you read WOIAF or Sworn Sword, you get a very clear picture that the Kings of the Rock and the Kings of the Reach were pretty bitter rivals, to the point where the existential purpose of Houses like Crakehall and Swyft and Serrett in the Westerlands and Oakheart and Rowan and Crane and Osgrey in the Reach is to guard against the other in a long-running series of border wars all along the “Northmarch.”