To reply directly to your question, as to how is a hard landing actually determined, this actually happened to a guy I know on the A-320. So, I suppose that my reply is type - specific, or, maybe operator specific.
His response was that, following an undoubted hard landing, in this case, the printer printed several pages of data, from the relevant aircraft sensors, and on-board computers. Data is then sent via acars to the Maintenance Dept. at base, and the required action taken.
In this case, the aircraft tells you!
