No, because Tywin was present for the Battle of the Mummer’s Ford:
“Father must have known that, because he sent out some men to oppose them, under the king’s own banner. He gave the command to some southron lordling, Lord Erik or Derik or something like that, but Ser Raymun Darry rode with him, and the letter said there were other knights as well, and a force of Father’s own guardsmen. Only it was a trap. Lord Derik had no sooner crossed the Red Fork than the Lannisters fell upon him, the king’s banner be damned, and Gregor Clegane took them in the rear as they tried to pull back across the Mummer’s Ford. This Lord Derik and a few others may have escaped, no one is certain, but Ser Raymun was killed, and most of our men from Winterfell. Lord Tywin has closed off the kingsroad, it’s said, and now he’s marching north toward Harrenhal, burning as he goes.”
So it is absolutely not the case that Tywin tried to recall Gregor; rather, Tywin was the anvil to Gregor’s hammer, and the two of them were working in concert to hit Beric Dondarrion’s forces from two directions at once. Yes, Tywin was pissed that Ned wasn’t there in person so that he could force the fait accompli, but that wasn’t enough to get him to call the whole thing off. By this point, he’s already committed to war against the Tullys as revenge for Tyrion’s capture and isn’t blinking at the idea of attacking the King’s banner in the process.