He doesn't have much of a choice Hitler holds all the cards.
in OTL, yes but not here
As popular Hitler rise to Power, the conservative were divided and thinking "That Mister Hitler is easy to spoof" oh boy were they wrong
The Military supported Hitler who wanted rearm Germany.
Also the Economic leaders of Germany wanted Hitler for similar Reasons and Fear of Left and Communist.
and there is Issue that German people wanted the Emperor or Strong Leader that return Germany back to it Old Glory
Something Hitler gave excellent to the masses "I'm strong Leader, under my rule we conquer the World"
But here in my proposal Willhelm III goes into Politic, things change allot.
Here the Crown Prince of Germany return to Power, allot Germans will be enthuse about this.
and Hitler popularity get first dents
like i have wrote the Military would support only Willhelm III, seeing now in Hitler only as necessary evil or Plan B.
and Hitler losing this trump card.
also in assumptions that Willhelm III manage to unite the conservative and Right-wings Parties
with backing of the Economic leaders of Germany, who consider now NSDAP as socialist menace
here Hitler losing last of his cards.
Hitler NSDAP face a union of conservative who consider the party, only as necessary evil to rule as coalition in 1930s.
The Chance is realistic that Willhelm III order the Police and Military to terminate the Communist violence and NSADP attacks on Jews
and bring back Law and Order on streets of chaotic Weimar Republic.
And Wilhelm has nothing to pressure Hindenburg with. Hindenburg will just deflect anything by arguing he must first save the country before doing something else. Hindenburg served his own interests first and above all else.
The Issue with Paul von Hindenburg is, the General was 85 year old in 1932 and wanted to retire from politic, but conservative politicians persuade him to run for another therm.
There is realistic opportunity that Von Hindenburg quit the Race in favor of Willhelm III and goes into retirement
but there many what if in this proposal and quite interesting ones
Like Reichs president Willhelm III vs Reichs chancellor Hitler