How does Austria unite Germany in this case?
Economic participation in the German Custom Union, liberal attitude to Hungary and Italy by not trying to remove autonomy or just by avoiding being dick towards local people.
For example the German economist Friedrich List manages to make the Frankfurt Diet accept his petition of complete German Union and the Austrians are willing to be part of it, this would remove some of the economic strength of Prussia and make Austria and allies better coordinated in a war by avoiding economic problems with Prussia boycotting them.
During the Springtime of Nations, not sure which year it would be butterflied, the Big Germany solution is enacted with much support from the Parliament and it offers the German Crown to the Austrian Emperor Ferdinand I, he accepts and with support of Rhineland´s rebels and with Berlin sieged by its own citizens and without much of the pressure from the Italian and Hungarian revolution the Austrians manage to led the Confederate German troops to victory against Denmark and Prussian reactionaries(again, if no butterflies in between) and to proclaim a pseudo-liberal German Empire. Hungary has his border revised with Germany and it becomes militarly, diplomatically independent but it has to renounce to Croatia that becomes a separated kingdom under a Hapsburg noble but still independent. Galicia-Lodomeria would either become Russian or sort of vassal, probably Krakow would be annex by the Russian. Bukovina would either become Moldovan/Romanian or more likely a Hapsburg/Russian vassal to pressure the Ottomans. Italy is a mess but maybe the Hapsburg could led a Italian Confederation of Hapsburg led states but without Piedmont and South Italy and the Papacy.