Originally Posted by drolldurham
an example of a two-notched, irremovable freewheel made by falcon:
image from park tool
I've had to deal with those before. It is a pain. If you can get a bolt on the end of the axle to hold the tool against the freewheel, it's much better. I loosened up the cones and moved the axle over to give myself enough length.
Really, this is emblematic of why bike shop mechanics hate wallmart-style bikes.