My pedals suddenly began wobbling from side to side, so I decided to just completely replace the bottom bracket. The struggle that followed cost me hours and only left me with a broken tool. The bottom bracket hasn't budged at all. I'm literally about to salvage parts from my bike and throw the frame away at this point. There is one last thing I want to try first, but I'm not happy about it. Looking for feedback and advice. Here's my journey:

I did my best to remove the dirt and grime with a toothbrush, spray it away with compressed air, get into the crevices with something small, and lubricate it with some WD-40.
Then I inserted this piece (don't know what it's called in English, so I'll just refer to it as "aftrækker" from here on) into the bottom bracket. It fit well and the hardened steel also stood up well:
So far so good. Unfortunately I don't have a big enough socket wrench or even regular wrench so I used my water pump pliers to hold it:
With that, I could get a very good grip on the aftrækker and I tried to turn it counter-clockwise (since I was working on the non-drive side) but it wouldn't budge. At all. I used all my strength, different angles, I hammered on it, I stood on it, I stomped on it. But nothing. I carried on for a long time, and eventually my water pump pliers got worn out and even broke!
Well, that's a shame because I'm not rich. And shortly after this, I gave up for now. My plan now is to buy a bigger socket wrench with a bit that fits around the aftrækker. This is turning out to be an expensive endeavor because I'll have to invest in new water pump pliers too (it's a great tool that has gotten me out of many hard spots so I gotta have it around). And it might all be for nothing, as I'm not very confident that anything will work at this point.
So my question here is: considering the story I just told, do you think I have any chance with a socket wrench or am I just wasting my time and money? Any other ideas?