I think the first part should contain "Fenians and your clans" rather than what you have--

I agree that "The peelers chased him out of Connemara,"

I thought it was "For beating up the bailiff's man O'Hara"

Castlebar (in Mayo) rather than Castlegar?

"Seven hundred peelers couldn't match him,

The chief sent out the orders for to catch him" ?????

Isn't the last line

"And the name of Paddy Mulligan, the girls of Ireland sigh!"