ETA: Many thanks to
lizbetann who found:
A Dog on Barkham Street and
The Bully of Barkham Street both by Mary Stolz.
/ETA
Okay...I'm feeling dumb for not remembering this.
Both Judy Blume and Beverly Cleary wrote series of books set in the same universe; Blume wrote Tales of a Fourth Grade Nothing, Superfudge!, Otherwise Known as Sheila the Great while Cleary wrote the Henry Huggins and Beezus and Ramona books.
There was a pair (or trio) of books that I thought was set in one of these universes (I THOUGHT it was in a sequel/parallel text to Tales of a Fourth Grade Nothing) where a similar chunk of time was told from the POV of the arch-bully on the block/at the school. Or maybe that was in the Henry Huggings series.
At any rate, in the story from the bully's POV, readers learn that the bully's parents fight all the time, that he has little money, that he is aware of his poor impulse control and hates himself for it, that some of the most vicious incidents in the other book(s) occur the week the parents take away his beloved dog because he's not adhering to the care expectations they outlined...
I remember the stories from the book, and wondering if the kids picking on me were similarly miserable, but I don't remmeber the name or in what series it was (or if it was an entirely different author than these two altogether.
Anyone else remember?