Stefan's answer sums this up nicely but I would just like to add that Tyrion's position as Hand of the King was given to him on a temporary basis by his father anyway.
Tywin was named Hand of the King following Eddard Stark's death but as he was out fighting Rob Stark's army he could not attend to the duties of the Hand and so took advantage of Tyrion's intellect by telling him to take the position on his behalf whilst he fought the war. When Tywin returns to King's Landing to save them from Stannis, he assumes his given role as Hand while Tyrion is resting.
Tyrion was Hand only on behalf of Tywin, Tywin has therefore always been Hand despite his absence from King's Landing. Tyrion should have been honored for his role in the battle but Tywin's contempt for Tyrion is boundless so he seeks to convey his late arrival as the heroic part of the battle and overlook Tyrion's merits.
Tywin sees Tyrion as an expendable resource. He knows Tyrion is skilled at manipulating people which is why he uses him in the first place but he also knows that King's Landing is a mess with the Crown half in debt to Tywin and knows Tyrion will remove some of that for him but he intends to show himself as the savior of the capital. The only thing Tywin couldn't predict for his son is what happens at the end of S4.