Hitler was in desperate need of resources require to continue the war, it wasn't just about ideology differences. What I am saying that he didn't assume the consequences the Germans would have to face, when fighting on two fronts and by that I mean his decisions to attack USSR and after few months declaring war on USA. Basically declaring war on every major power since Italians were not that much effective and Japanese were miles away to assist their allies. None the less, the dire need for resources required for offensives, not enough production of military equipment as compared to their counterparts, code breaking by allies of incoming enemy operations and shortages of supplies due to harsh weather conditions and naval blockades.
Invasion of Yugoslavia was essential for Germans since Italians were losing ground to Greeks in Pindus mountain and were pushed back all the way to Albanian border. Moreover, Italians were also being beaten back by British in North Africa. So Hitler had to make a move in supporting his ally and secure his position in Balkans to initiate Operation Barbrossa.