Given the repetition of the name Nelson, I think it's very likely your Aldriches are cousins of mine, Carole.
The reason I think so is because the Aldrich line (Nelson Wilmarth Aldrich's daughter Abigail, to be exact) married into the Rockellers and the name Nelson was also passed down in that line, as well (Nelson Aldrich Rockefeller, former Vice President of the United States, under Gerald Ford). Nelson Rockefeller's younger brother is David Rockefeller, founder of the Trilateral Commission. Abigail Aldrich, Nelson Wilmarth Aldrich's daughter, married John D. Rockefeller, Jr., the son of the founder of the Rockefeller dynasty, John D. Rockfeller, who founded Standard Oil. Recall your high school history for the term "robber barons," and you've got the picture (or some of it, anyway).
What your line's exact connection is I'm not sure, though.