AFLM's stoves reminded me of the old cast iron wood fired stove in my Grandparent's home that they were still using up until the mid-1950's. It had an oven and "cook top" and also served to warm their house.

Functionally, it sounds like this might be what your Mom is thinking of.

A quick Google search for "old fashioned wood burning kitchen stoves" revealed that various versions are still being made.
For example:
http://www.elmirastoveworks.com/fireview/ and
http://www.antiquestoves.com/general%20store/generalstore.index.htm

(no affiliation)

I have seen similar concepts built out of brick (fire brick and red brick).

Costs and installation (perhaps on the porch) might be prohibitive, but they can last a lifetime.