It doesn't sound particularly offensive to me. Are they actual furries (people who cosplay as animals), or anthropomorphic animals (like Mickey Mouse, or Roger Rabbit)? Some people are offended by furries, but hardly any one is offended by an anthropomorphic character.
Also, is your book aimed at children or adults? Animal characters are abundant in children's books, though less so in adults.
And you said the husband is attractive, and that might be offensive... By "attractive", do you mean he is actually having sex in the book, or is he just good looking? Fantastic Mr. Fox and many other animal characters were described as "handsome" or "dashing", and no one thought that was creepy. Depending on the tone of the book (humorous, or serious), people may or may not find a sexually active anthropomorphized cat offensive. Surely some people will, but you can't please everyone...
David Sedaris wrote book about animals, that was quite popular, and even featured topics such as dating.
If you can't find a publisher, maybe self publish? Quite a few people are doing it now, with the advent of e-books.