SS Freewheels can be difficult to get off (same as screw-on 5-speed).
You should use the correct 2-prong remover. A hammer & punch is quite likely to wreck the freewhee during removal.
The thread is normal right hand.
The easiest way to get it off is with the axle in place. Thread the remover over the axle with the dogs engaged with the two notches in the freewheel. Put on the wheelnut finger tight, then back it off 1/4 turn. Clamp the remover in a solid bench vice, and heave on the wheel rim to break the freewheel loose. Once it's started to move you can take it out of the vice, remove the wheelnut and undo with a spanner.
The two holes are for getting at the innards of the freewheel (bearings and pawls).