This is the name commonly used in Look to the West of the War of the Austrian Succession.
In most ways, it is very similar to the OTL version, with almost identical victories, losses and innovations. However, changes enter with the death of George II of Great Britain on the field of Dettingen and his second son becoming William IV. William went on to subdue the Second (and most successful) Jacobite Rebellion, led by Charles Edward Stuart.
It is with the unpopular peace treaty of Aix-la-Chapelle that differences set in. As in OTL, the idea of handing back the hard-won fortress of Louisbourg in North America is unpopular among the American colonists. However, in TTL the siege was in part commanded by the exiled Prince Frederick, who now acts as a charismatic leader to fight for American rights and regain his stolen throne.
Because of the ensuing War of the British Succession and the British refusal to ratify the Treaty, Britain retains Louisbourg and France retains Madras in India (resulting in the death of Robert Clive). However, France still hands back the Austrian Netherlands, which is the most unpopular decision among the French people, who invented the idiom 'as stupid as the peace'.
The Second War of Supremacy ultimately failed to resolve the ownership of Silesia between Prussia and Austria, and led into the Third War of Supremacy.