I read Mad Magazine religiously when I was a kid, I don’t remember Ugly Family as a one-time or a series. So I’m inclined to think that maybe Cracked had that feature. I always thought that Cracked was a cheap-ass imitation of Mad, anyway.

It was Cracked & I think the family disappeared back in the 80s. There was a movie in 1982. Not sure were you can find it, but I’m sure it’s just sitting there waiting for you to find it!!! ;-)

Edit: Looked a bit further, but the movie was a failed TV pilot.