Why did Hitler split army group south for the 1942 summer offensive?

If I understand correctly, the question could be told with following words:

• Why did Hitler specifically split the two groups rather than following initial plan?

Well, Hitler in 1942 started to play a very important role in German operations: In 1941, he was all the time "harassed" by his generals that wanted to be listened to. But in 1942, Hitler thought he had saved the Wehrmacht from destruction during the battle of Moscow by ordering an all-out resistance (this was not entirely true nor false).

With this situation in mind, think about 1942: the Germans are conducting a specific attack to capture oil and destroy Soviet forces, but the attack went bad: Soviet are escaping the circle, and the Caucasus looks open to attack. Hitler thought that the strategic target of oil was the most important (as he did in 1941), and that German troops were strong enough to resist in the North East.

So he split the group in two parts. And then he realized that reaching the Volga, especially in Stalingrad, was important so he sent the North-East branch, namely the 6th Army, to the city instead of asking it a defensive stance.

Then he had to send spare troops (Hungarian, Romanian, Italian), to fill the gap and this ultimately led to Stalingrad disaster.

So "**why did Hitler specifically" is answered by:

• Hitler was focused on strategic resources
• From 1941 events, Hitler thought he should go above its commanders sometimes and personally gives operationnal or tactical orientations

One has to understand that every day were changes in the german plan, often the plans were divergent and chaotic. So one can't make the assumption that germans were following a single action line, in fact, everything was micromanagement of Hitler or decisions made by the generals in the field.

I will put some examples taken from Halder's diary.

An example of generals ignoring orders from above

July 6: Von Bock, as usual, allowed his decisions to be guided by the ideas of his army commanders. The net result was that von Weichs was ordered to keep his forces mustered alongside his own northern wing and Hoth, in his anxiety, drew forces from XXXX Corps, while von Paulus, irrepressible as ever, simply stepped forward and overwhelmed the enemy. The army group command, which had been assigned a mission clearly directed to the south, sadly failed to exert effective influence to discipline these divergent spirits and align them according to the basic intention of the offensive.

An example of a major change in the battle order

July 13: The IV Panzer Army is placed under the command of Army Group A, with the mission of preventing the escape of the enemy to the east... Army Group B will cover the rear and flank of Army Group A.

An example of change of tactic

July 18: The Fuehrer surprises me when he approves the same recommendations of mine that he very impolitely rejected yesterday, preferring a plan that would have produced a senseless rally on the north bank of the Don at Rostov. And immediately his most magnificent order is given, arranging for the crossing of the Don on a wide front and the initiation of the Battle of Stanlingrad.

Another drastical change in the tactic

July 23: As a result of the concentration of the army that the Fuehrer ordered on July 17, in spite of my opposition, and after having diverted the 24th Panzer to the Sixth Army, a movement that he ordered on July 21, it is becoming obvious, even for an ignorant, that the Rostov area is crammed with armored vehicles that have nothing to do... Now that the result is so palpable, he explodes in mad rage and fires the worst reproaches at the General Staff.

A change of strategy after a month of battle

July 30: Jold talks: He pompously announces that the fate of the Caucasus will be decided at Stalingrad and, in view of the importance of the battle, it will be necessary to divert forces from Army Group A to Army Group B... This is a version spiced with the proposal that I myself presented to the Fuehrer six days ago.

So, one can see that plans changed all the time. I would say that, if germans would have had more time in the Don, probably they would have changed many more times their approach to battle.
After Groups A and B divert geographically, one to the Caucasus and other to Stalingrad, no more changes were possible, distance between them prevented any other change of strategy and forced them to work independently.