A very different Great War

[True Federalist (진정한 연방 주의자)]

An Anglo-Prussian alliance might have worked if Queen Victoria had instead been King Victor of the United Kingdom and Hanover.  If that pesky Salic Law hadn't caused the British and Hanoverian crowns to diverge, then either a German Empire doesn't emerge or it's a heavily British influenced one.

Alternatively, suppose none of Victoria's sons have children. (Perhaps they get caught up in a Mumps epidemic and are rendered sterile.)  While King William V would be on the throne when the war starts if there are no other butterflies, the Kaiser Wilhelm II would be his heir presumptive. (Tho if the various royals all still die at the same times as in OTL, it wouldn't be Wilhelm II who gets to be William VI, but his son.)

[True Federalist (진정한 연방 주의자)]

Wilhelm's father was likely allowed to marry the Princess Royal because she had four brothers ahead of her in the line of succession and thus was unlikely to inherit.  He was the eldest grandson even if don't butterfly the issue of those four, of whom two would be kings as Edward VII and William V respectively.  (I doubt Prince Arthur would dare reign as King Arthur, so I assume he'd use his second name just as his eldest brother did.  Conversely if the brother between Princes Albert and Arthur, Prince Alfred, had come to throne, I doubt he'd use his second name and reign as King Ernest, tho I would hope he would. )

If you want to have closer cooperation between Britain and Germany, you'd likely have to have Fredrick III stay on the German throne more than the mere 99 days fate allowed him.  That would be the case regardless of whether or not his son Wilhelm II ever became the British heir presumptive.

[True Federalist (진정한 연방 주의자)]

While it would have liberalized Germany slightly, the main benefits to improved Anglo-German relations would have come from a weakening of the military's control of the government and a less belligerent foreign policy.  Also, while Wilhelm II would still likely be a reactionary bastard, a decade or two of his father's rule might well have taught him some tact and kept him from making some of the blunders he did.

It doesn't need to be a major change.  Simply keeping the tensions low so that the British never plan properly for a BEF would be sufficient.  If the Germans don't support the Boers during the Second Boer War, then it goes more smoothly for the British and they see no need for the Haldane reforms.  An ineffective or absent BEF means France falls in 1914.

More significantly, if groundwork was not laid out for what became the Entente, it is possible that the Great War breaks out in 1904.  France was nominally the ally of Russia and Britain the ally of Japan.  It would not be implausible for them to come to blows then instead of a decade later.

[True Federalist (진정한 연방 주의자)]

Sorry BEF?

British Expeditionary Force  Even tho they got creamed in the process, they delayed the Hun long enough at Mons to allow them to be stopped at First Marne.

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Prince Henry was more liberal and more diplomatic than his older brother, but he also was a naval officer by profession and temperament.  If you're thinking of him taking the German throne because of some mischance happening to Wilhelm, I'm doubtful it would lead to improved Anglo-German relations because of the Navy being the sorest spot between the two Empires.

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The idea that the Hapless Habsburgs could create a united Germany in the 19th century is extremely far fetched.  It wasn't until the aftermath of losing the Austro-Prussian War of 1866 that they took even limited steps to realistically address the rising tide of nationalism within their multinational state and even that didn't really go far enough.  Not that I blame the Habsburgs too much.  It's hard to see how they could have done much better than they did under the circumstances.

[True Federalist (진정한 연방 주의자)]

What about if rights were given to different ethnic groups or something caused national unity to placate them; allowing peace at home maybe allows time to think about a unified German state?

If they did that, which I don't think they could have, even if inclined to do so, the Hungarians would have been most upset with that.  In many ways, the Hungarians were even more chauvinistic than the Austrians.  Plus it wasn't really in the interests of the Prussians, Russians, or Austrians to let the Poles have any sort of effective autonomy.  The Poles were in many ways the Kurds of the 19th Century.

But even if they were somehow to do all that, you're still left with the problem that Austria is effectively doomed to lose the Austro-Prussian War without rewriting a whole lot more history. At a minimum, you'd have to scrap the Congress of Vienna and have something else put in its place after Napoleon's final downfall.  (Assuming there is a final downfall.)

[True Federalist (진정한 연방 주의자)]

What about if rights were given to different ethnic groups or something caused national unity to placate them; allowing peace at home maybe allows time to think about a unified German state?

If they did that, which I don't think they could have, even if inclined to do so, the Hungarians would have been most upset with that.  In many ways, the Hungarians were even more chauvinistic than the Austrians.  Plus it wasn't really in the interests of the Prussians, Russians, or Austrians to let the Poles have any sort of effective autonomy.  The Poles were in many ways the Kurds of the 19th Century.

But even if they were somehow to do all that, you're still left with the problem that Austria is effectively doomed to lose the Austro-Prussian War without rewriting a whole lot more history. At a minimum, you'd have to scrap the Congress of Vienna and have something else put in its place after Napoleon's final downfall.  (Assuming there is a final downfall.)

What about Prussia turning the Austro-Prussian War into a War of Conquest, conquering all Habsburg lands?

The Prussians weren't that crazy.  If it had been feasible to take just Austria and Bohemia, then just maybe.  Or perhaps have Maximillian or Karl Ludwig instead of Franz Joseph be named King of Bohemia when their uncle Ferdinand abdicated in 1848.  (They were a little young, but their father Franz Karl could have served as a regent to oversee the orderly breakup of the Habsburg empire into nation states as a result of the 1848 revolution.)