could someone with a good understanding of the story give me a summary of what is happenin...

I believe that law is just remembering the past

So I believe it's Law's remembrance of their past interactions that lead up to the scene cut-off from when they were adults. This arc delves into why Law became the way he is with Jesse and what happened with Moritat. With the most recent update, Law has finally found a weakness (or doorway) into the lives of the Browns which his parents have forced him to do. In the beginning, as children, Law became close to Jesse because his parents forced him to. However, as they spent more time together and Jesse began to accept him more, their relationship became more tat formalities. But, in the back of Law's mind, he's always been trying to search for an upper hand with the Brown (mostly because of his parent's insisting him do so). I hope that helped ?? （￣へ￣）

it did, thank you :)

I don't think so. Law is trying to search for the upper hand on Jesse, not the Brown family. His mother even told him that he can stop meeting Jesse. But he insisted on continuing to do so and that's because of his obsession with Jesse. Not because he's told so.

I agree, though judging by some of the events in Moritat (where their actual experiences were swapped), I'm guessing that Law accidentally leaked the brown family's medical condition. Also I the mum only told Law to stop meeting with Jesse because she was afraid that Law was becoming more dependent on Jesse's affection rather his parent's. In chapter 42 she's went back to her old self in the scene where Law was sick in bed (caring more about the staying close to the browns, than her son's own well-being).

Yea, exactly. Law and Jesse's relationship is obviously twisted and multi-layered. But I think that's kind of the gist of it.