How did the politics work of the between these two? austria was part of the HRE but Hungary was not. how were the political interests of the leader of the austro-hungarian empire reconciled with half his empire being part of the the HRE?
i might have gotten this all wrong. can you point me to somewhere i can read or if someone is gracious enoughto explain id be grateful . thanks
A few things, first the House of Habsburg held the Kingdom of Hungary as part of their crown lands which were taken from the Ottomans during the 17th and 18th centuries. Formally there wouldn't be any sort of non-Austrian government of Hungary until after the Napoleonic Wars.
Most importantly, the Holy Roman Empire was dissolved by Napoleon during the Treaty of Pressburg after the defeat of Austria in the War of the Third Coalition. Generally you are melding the Holy Roman Empire, the Austrian Empire, and the Austro-Hungarian Empire, but considering how nonsense the politics and history is, it's completely understandable.
For reading, I'd recommend The Habsburgs by Andrew Wheatcroft.