Disagree Super T.
Tywin, while of a different personality than Tyrion, was his political match in every way, and far more established.
If the Tyrells were going to cut the head off of the machine that is the Lannisters, you hit Tywin regardless of what he's doing at the moment. Tyrion hadn't even been recognized by his own family, nor the other royals, as being that important. Yes, he was hand, but only in the absence of Tywin.
Tywin had no choice in making him Hand either, he was clear about his views of women in politics, a la Cersei, and his other son was...well, too many issues, and he probably knew Jaime would deny the post by virtue of his past decisions.
Tyrion hadn't really displayed that level of strategic acquity until that battle.
He was an unknown, while Tywin was a very well known commodity, as was Cersei.
If the Tyrells were going to target a Lannister, it would either have been Tywin or Cersei.
It had to be Cersei that put the hit out for Tyrion.
This is a very, very inaccurate quote from The Usual Suspects, but it goes something like this:
"With cops, if they think the boyfriend killed the girlfriend, 99 percent of the time they're right.".