Mysha,

Well done on a good attempt at explaining the spirit of the song.

To say that a Stater wanted an Irish Republic would cause something of debate here. They were prepared to accept a limited form of freedom in which the twenty six counties had self government but within the British Commonwealth and (this was a big issue at the time) swearing an oath of allegiance to the British Monarch (a King at the time). The other side in the Civil War who regarded themselves as the true Republicans were not prepared to accept a traty on those terms. Eventually the majority of them accepted the free state, came into power and changed the constitution in 1937.

A digging match and a jar - You're right about the jar but the digging match would be fists not clubs.

A pretty difficult song to understand if you don't know Dublin and in particular Dublin of the 1950s and 60s.