Yes, between the two of them, Ludendorff was the one with the ideas, but it was not politic to say that. See, Hindenburg was the public face of the duo. Indeed, he even got his own cult of personality. His popularity surpassed that of the Kaiser. Successes were attributed to him, failures blamed on other people. The Hindenburg cult was so successful it survived the war, when the terrible two managed to blame everything that had gone wrong on 'backstabbers'. So when Ludendorff turned on Hindenburg, he committed a big faux pas.
Ludendorff was very unhappy when Hindenburg entered the election for Reich President, and broke off relatons with him. He even refused to stand besides his former boss at the dedication of the Tannenberg memorial, and aggressively attacked him in the press with hate-filled tirades. None of this was a good look.
As for Ludendorff, in OTL he died of liver cancer in 1937. By then he was 72 years old. I don't think butterflies would change that much. In OTL Hitler was interested in using for propaganda purposes after he'd consolidated power. But assuming everything else remains the same, Ludendorff agreeing to that will probably change little.
That said, I'm not ruling out an alternate scenario where Ludendorff doesn't become a joke, though I don't think that's compatible with a scenario where everything else stays the same. He was originally quite important in the far right. Back then, the Nazi party was just one small fish in a big pond. Ludendorff's 60th birthday was celebrated by massed bands and a parade, and that was after the failed coup. It's been speculated that Hitler encouraged Ludendorff to run for president in order to undermine him. It certainly damaged his prospects quite seriously (he got 1.1 per cent of the vote), as did writing angry tirades against Hindenburg and going off the deep end to a point where even Alfred Rosenberg, who's the exact opposite of a poster child of lucidity, thought he was weird (pot, kettle, I know!).