Yes, the war cabinet wanted the excuse to do what they have always planned to do, and there is some evidence that they set up the excuse.

HAMAS is an acronym for Ḥarakat al-Muqāwamah al-ʾIslāmiyyah, and their militant unit is the Ezzedeen Al-Qassam Brigades. Mostly people mean Al-Qassam when they say Hamas, but they say Hamas since Westerners don't usually make the distinction from political Hamas and military Hamas.

I always remember something after I post that adds more subtelty and context. Many rockets from S. Lebanon were targetted well enough to take out iron dome sensors and such. And many were not towards anything in particular, just designed to trigger an iron dome response in order to deplete the iron dome.  So I shouldn't say they were all war crimes.  Some were.