That is an early threaded coaster sprocket. It is unique to American hubs (New Departure, Morrow/Bendix). If you don't have a replacement, don't remove it; they are very difficult to get off, and modern threaded sprockets do NOT fit. You can rebuild the wheel simply by removing the axle/driver assembly.

They are on super tight; It is a consequence of them being handmade, you see. The threads on both parts are quite tall, which leads to a boatload of friction when they are tightened. The standard way of dealing with it back then was one of two ways:

1) Replace the driver assembly with the new sprocket

2) Remove the sprocket with whatever you had at hand.

Unfortunately, as you've found out, that's not always easy...I've failed entirely using a 2 foot-long chain whip. In order to preserve as many rare parts as I could, I wound up splitting the sprocket by cutting a slot as far down as I could, then splitting it with a chisel. It still required all of the two feet of the chain whip's handle to remove it. I've heard stories of one person who had access to a large machinist's lathe, who chucked the driver in the jaws, and using the brake, was able to reliably remove the sprocket with a chain whip. Of course, at that point, it would almost be easier to simply cut it off with the lathe.

Since 1) was such a popular option, it is possible to find NOS drivers, if you keep your eyes open.