I don't see Ludendorff being anyone's puppet. Ludendorff and Hitler were alike in many ways. They despised Jews and Christians, they both wanted Germany to rearm, with Ludendorff even literally writing the book on total war.
But, Hitler and Ludendorff would be bitter rivals for the leadership of the party. Ludendorff would be a threat to Hitler's place as leader of the Nazi Party, since he, unlike Hitler, is a military officer with some serious pedigree. While Hitler, as leader of the Party in OTL, pandered to the German working class, Ludendorff stuck to circles involving the military and this behaviour would continue during Ludendorff's presidency, with him pandering to the German officer corps and their soldiers to give him weight in a possible contest with Hitler. In our tmeline, when Hitler became Fuhrer, he forced the German Army to swear a oath fo allegiance to him alone, thereby securing their loyalty. With Ludendorff as president in this timeline, that's going to be almost impossible to do, so the Army's loyalty would be in doubt.
Hitler can't just 'Operation Hummingbird' him. He would have to work to undermine Ludendorff's support in the military, maybe telling the German industrialists. 'If you don't get the Army on my side, I will make your life hell'. Whether this will work or not is debatable. But he would have to make Ludendorff look weak without making the Party look weak.
I don't see how this could turn out. Either Ludendorff wins and knocks Hitler out for good or Ludendorff is forced to resign the presidency.