Ron Rosenbaum's superb book on the Munich years, "Explaining Hitler" made a persuasive case for Hitler having killed her in a jealous rage, the evidence he cited made that more likely.
If we look at other such organizations then and now, they often do collapse when the charismatic leader's crimes catch up with them, and rarely regain their former power and prestige. The degree to which the Nazis had already seized the criminal justice system and newspapers in the Munich area (through assassinations, kidnappings, assaults, arson, etc. as Rosenbaum details in his book), a scandal is still probably averted with "just" Hitler out of the picture.
Or someone in the management team steps up quickly (sometimes with a grin that suggests the scandal coming to light wasn't entirely random) which seems more likely given the Nazi's hierarchy already as a criminal organization legitimizing itself into a political movement. The team that had coached and trained Adolph was still quite present and another front man wouldn't be hard to find among the many World War I heroes. Chances are good the replacement would be less crazy and more compliant with the handlers than Hitler, learning from their previous mistakes, but less likely to gamble on his intuition or "will" so much. So World War II starts in the mid-1940's when the High Command thought they could be sufficiently prepared and with resource stockpiles far greater and on a more muted scheme that still catches the neighbors by surprise but engages far fewer of them.
Hitler always looks like the better choice for an enemy than a sane, careful nemesis.
Who other than Hitler would have remilitarized the Rhineland and annex Austria? A more cautious German leader may have tried these things later, but with the Great Depression dissipating will run into more resistance. Hence, while Hitler got these things "easily" a more cautious leader would expand much more slowly and not unilaterally.
In retrospect, Hitler was a craps player who kept throwing sevens. He had a ridiculously lucky run. So, a different leader probably fails to annex Austria, and probably ultimately avoids war because without Austria and Czeckoslovakia he would be nuts to risk a general European war.
This is why I see such a Germany working very closely with the USSR in the 1940s simply because it works for Russia to use Germany as a shield between them and western Europe, and it works for Germany whenever Germany begins a process of expansionism. Germany would probably seek mutual defense with the USSR and have something of an expeditionary force and a beefed up Westwall. Italy probably joins the Allies to check German and Russian expansionism in South East Europe. Hungary probably joins the German camp to maintain the integrity of their borders against the Russians. Romania may be coerced into a do-nothing alliance with the Germans as they did OTL, because joining with Italy would prove suicidal given their borders, even with British and Romanian support.
All in all, once the nuclear age begins, it is very possible that there really isn't a World War II, because a more cautious Germany and the ATL USSR would probably take until the mid 40s to gain the concessions they wanted in central and South East Europe. At this point, the US finished of Japan, the USSR probably takes slim pickings, and Germany is dragged into a cold war against a Nuclear power (probably becoming one themselves soon after.) THe question then becomes how much better the Soviet-blocs rocket and aircraft technology is going to be with Germany absorbed into their sphere.
The only way out is if Germany switched sides with the West, which is possible and World War II is essentially a crusade against Bolshevism. But, at this point, it would be the mid 40s.