Having spent some significant time taking bits of bikes apart when I was younger, my experience is the opposite of David's. My experience is that freewheels are very reluctant to move when applying a hammer and drift to the "two dots". Especially if the wheel and freewheel have had years of being married together, they'll seriously resist divorce. And if you hammer in the wrong direction, that plate with two dots is a cover for the ball races and you'll have a floor full of tiny ball bearings.
I'm going to give you a slight frame challenge instead. If this is an old bike, I would not be at all surprised if the wheels were steel, or at best some low-grade alloy. The spokes are probably in a bad way, and you don't really want to be stuck with an old-style freewheel anyway. If you're planning on chucking the freewheel anyway, why not chuck the whole thing and buy a decent new alloy wheel and cassette? No need to remove anything.
Don't forget that you want a new chain as well, whatever you do. Chains wear into the geartrain, so if you change the cogs then you should change the chain too. They're pretty cheap anyway. You'll need a chain remover tool if you haven't already got one, of course.