How often my wife was at me about that projected grand entrance-hall of hers, which was to be knocked clean through the chimney,
What is the meaning of the highlighted section?
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"clean" is used informally to emphasize that something was done completely, thoroughly (definition 12). "clean through" is similar to "straight through".
It seems that the wife wants to build a grand entrance hall through where the chimney is. The chimney will need to be demolished.