Well, I think first you need to look at the concept of this being "Disney related without going to a Disney Park". Unless you do one of the 2 itineraries that actually go to a Disney Park (Southern California & China) or the one that goes to the Walt Disney museum (San Francisco weekend), the Disney relation here is in the quality of the itineraries, and the excellent training of the Adventure Guides. The trips themselves are not "Disney related", which is one of the things I really like about
ABD. They are, in general, amazingly un-Disneyfied. I had to convince my friends that I was not going on vacation with Cinderella and Mickey Mouse. Really, the only Disney element to the trips, besides the quality, is the daily themed pins you get each day of the trips. As long as you are good with that, you should be great with any of the itineraries ABD offers, based on what your family likes and has an urge to see.
If you think your family won't like something not really "Disney related" you could try the Southern California Backstage Magic ABD, which *does* include a lot of Disney aspects (Imagineering, Disney Studios,
Disneyland, etc). If you like that one, and how ABD operates, then you could look at doing one of the other trips (and Italy is a good one to start with).
I hope this makes sense.
If you let us know what your family is like, what they're interested in, how they travel, etc, a lot of us could probably come up with some suggestions for you.
Sayhello