I killed the three random people to join the Brotherhood, then walked around on some other errands. I got the letter, but in another province. I go back, but then I get a letter that references the other province with a town name that doesn't exist there. I was forced to let the quest fail but I still want to join the Brotherhood. Can I use a console command or something?

And sorry if I am not coherent, I am far too tired to be doing this.

No, there's no console in Daggerfall. Once you miss the opportunity with DB, you miss it. Same is with Thieves guild. Unless you have an earlier save, you're out of luck.