So you're telling me he's adept at both politics and combat because his son rebelled and he went along for the ride, then when Renly died and Littlefinger arranged for him to not get executed for treason, he agreed to it?
Sorry, not gonna agree with you on that one. Essentially, he picked the biggest army each time. He's lucky no one killed him for being a faithless snake.
Funny, but for his third son to join Renly pretty much doesn't require him to do anything. Wilas is his heir and Ser Garlan is his second son and best swordsman. Loras is unlikely to ever become a Lord if married to a woman, unless of a very minor house. He married Margaery off to someone who he thought could unite the Seven Kingdoms. That was a big power play.
Because Renly died and none of his Knights or soliders died with him, it was wise for Lord Tyrell to withdraw and regroup to figure out who could give him the best deal. While Littlefinger went to him from KL, he also sent Lord Tarly, one of the best soldiers and battle commanders, to parlay with Lord Tywin. It was clear he had Tywin b/w a rock and a hard place. Tywin was vulnerable to being trapped between the Tyrell forces and the Stark/Riverlands forces behind him. Remember, Robb was trying to trap Tywin, but Edmure screwed it up. Without making a deal with the Tyrells, Twyin was trapped, could not reach Kings Landing unmolested, and could not protect his grandson from Stannis.
And, his army was as big as any other. The Reach is plentiful with both people and resources. Meanwhile the Westerlands were being savaged, so Tywin was weaker. And, the Tyrells are close in finances to the Lannisters.