It's a little like remarriage after a spouse dies. Sometimes it comes quick, other times after many years, and some never remarry. Brian was a dog with human qualities- he ate at a table, slept with human women, and was a stinkin' drunk. It's no surprise the very idea of Vinny existing puts off a lot of the fanbase.
The real problem's this show's dyslexic drama; they want it to stay a comedy, so they had to cut the Griffin's mourning down with a timeskip and replace him immediately. But they also want this to have gravity, which is hard after they've joked about every character dying in some way and waived off plotholes that would make the audience incredulous in any other setting besides a self-aware cartoon. It's a bind of their own making that would've worked better before MacFarlane split his focus between three shows.