It turns out that there is a technique that involves using a bolt, a bunch of washers and a screw with a nut that can be purshased from just about any hardware store. The technique is documented here.
I tried it out and it worked like a charm. Even then, it's the amount of leverage you gain access to that makes all the difference(used a cheater bar for more leverage). The cap(drive side) happened to unscrew clockwise, same as the other one(Once I had the non-drive-side cup removed, I slid my finger along the threads of the drive-side around the inner perimeter to see if my finger was being pulled inwards or outwards to figure out the threading).
I also struggled because unbeknownst to me, my dad literally screwed a screw through the frame to lock the cup on the non-drive side. I used pliers to twist it out.
This was a satisfying experience.