Just so you know, we actually know very little about the details of the Akō incident (the proper term for the 47 ronin) due to a publication ban by the Shogunate. Lots of what you know are from fictional accounts of it. We actually do not know of the motivation of the 47 (indeed, it's a topic heavily debated by scholars of the time), and it is fairly likely that not all 47 had the same motivation. However, as the 47 were not blood relations of Asano, technically it wouldn't be a blood feud.

As for the question itself, there were definitely "rival" families. Therefore I would be very shocked if there weren't families with some equivalent of blood feuds (at least temporarily, but would that still qualify?). But that's the extent of my knowledge.

The Tokugawa Shogunate's solution to preventing violence from a group of heavily armed men who's been fighting for over a century is to import and heavily sponsor Neo-Confucianism and merging it into samurai thinking, turning them into bureaucrats. More radical (ie violent) philosophies were discouraged. Even following your lord's death with suicide was banned, which lead Yamamoto Tsunetomo to write the Hagakure (which was also banned).

The law itself strictly disallowed private fights. Daimyos could get a fief reduction or even broken up and taken away (though I can't find a written policy on what the punishment actually would be, but it's clearly stated it's not allowed). As for commoners, the law actually states if some fight occurs with weapons, the entire village would be punished. That's actually in line with the idea of mutual responsibility common in East Asia of the time.

However, interestingly, it would appear that revenge killing would be permitted if and only if the original victim was an elder direct relation, usually a father, and the perpetrator had gone unpunished by the law. 118 revenge killings are recorded in the Edo period, of which 115 are such killings.