In mid-summer 2013.....I started to pick up six different books going over WW I, the Kaiser, the 1800s Germany, and the general culture of the period around the war.
There is no doubt that WW I resets German politics and puts a harsh reality upon most Germans. The Germans without the war, in some 'what-if' situation?
I have no doubt that a Kaiser-dominated German government would have continued on, with Prussian military authority as a key part of the government.
If they'd avoided using the Austrian assassination as a lead-in to a European conflict.....I think they would have simply found another episode three years or ten years later for some orchestrated conflict to tie up loose political issues within Germany.
A smaller and more direct conflict....just against Austria, or just against Russia.....might have prevented the massive world war scenario.
Few people realize that the Kaiser, after leaving Germany in 1919, survived on til 1941 in Huis Doorn, Utrechtse Heuvelrug, Netherlands....his health only declining in the mid-1930s.
The son? Wilhelm III? Well, this gets into an interesting side story. The crown prince was already noted in 1901 as heaving a healthy appetite for women (numerous women in fact).....at the age of 19.
You can go through the next twenty years and find that Wilhelm III's chief interest was soccer (he helped in the start-up of the German Football Association in 1908 (he actually paid for the cup to be awarded) and tennis.
What happened after the family was sent out of Germany? This gets to being interesting as well. Wilhelm III got into German politics....at least in the discussion of such things. By 1932, turning fifty....he actually got into some talks of running for the office of Reichspräsident, under the umbrella as a right-wing candidate. The opposing and assured winner was Paul von Hindenburg. For some reason, Wilhelm III's father got into this discussion and really didn't want the son (as royality and assumed prince-to-be-Kaiser one day.....to be an elected official. So he dropped out.
It should be noted....for the 1932 election....Wilhelm III strongly endorsed the Nazi Party.
Two years would pass after the Nazi win in November of 1932, and the night of the "Long Knives" occurred. A friend and associate of Wilhelm III.....Kurt von Schleicher....former Chancellor of Germany....was assassinated by Nazi enthusiasts. Wilhelm III had known von Schleicher for years and this one event changed his entire perception of the Nazi rise to power.
From 1934 on....Wilhelm III simply stayed in the background and never really participated in any government talks. The rumors of Hitler before 1934....that maybe the royal family could be brought back into Germany and be part of some future monarchy? Simply rumors.....they never went anywhere.
Wilhelm III, without the WW I conflict? He would have been there in 1941 to assume the position of Kaiser.....at age fifty-nine years old. He might have been a different style of Kaiser, and maybe by this point....smarter than his father.
It should be noted....by early 1945....Wilhelm III had serious health issues (gall bladder and liver). One might guess that he had a fair amount of alcohol consumption throughout his life. And he ended up passing away ten years after his father. His last six years was mostly as a war criminal and held under house arrest....never being charged but never being allowed any freedom.
Germany has a a number of positives and negatives without WW I. The US depression period (which has a world effect) would still affect German economics, and bring a harsh reality into Germany for the 1930s. Without WW I, there is no WW II. Hitler? He probably ends up married in the mid-20's to some Munich gal with a taste for culture, running some house-painting service, and often hanging out at art museums in Munich to criticize modern art.
What-if situations are always curious to lay out, but they never seem to really answer any questions. We are left with what did happen.