Yes, you've got it. I would probably translate it as:
There are some people who say they look like dogs or cats, and there are others that say they look exactly like the master of the house. (or, spitting image, as you wrote).
Or;
There are those who say they look like dogs or cats, and there are still others who say they look exactly like the master of the house.
"Master of the house" is a bit old fashioned, but in lieu of a better term I think we're stuck with it. Head of the house, maybe?