There was no real problem with a woman inheriting the Austrian throne. But it could be a useful pretext for war by nations keen on advancing their own interests militarily. Frederick II of Prussia was quick to go to war - the Philosopher Prince became a Military King when he had the power to  - and he seized the rich Austrian province of Silesia (which is actually Polish, but neither the Austrians nor the Prussians cared about that).

Britain kept fighting the War of Jenkins' Ear against the Spanish, but then it got subsumed into the War of Austrian Succession, which it joined on the Austrian side as it had in the War of Spanish Succession. It did badly in the land war, under George II who, at Dettingen, became the last British sovereign to appear on a battlefield, and his younger son, the Duke of Cumberland, who proved pretty hopeless. They fought the French in America, chiefly through the Massachusetts colonists, and in India, through the East India Company.

Most gains were handed back at the end of the fighting, except that Prussia hung on to Silesia. With British backing. Which annoyed Austria a lot, and that had consequences for the next war. A war that was bound to come, since this one had sorted out very little, apart from allowing Maria Theresa to mount the Austrian throne after all.

Illustration: Empress Maria Theresa, portrait by Martin van Meytens, 1759. Public domain (published anywhere (or registered with the U.S. Copyright Office) before 1926 and public domain in the U.S.)

Music: Bach Partita #2c by J Bu licensed under an Attribution-NonCommercial-No Derivatives (aka Music Sharing) 3.0 International License