I think I might have made sense of this sentence. Tell me what you think:

The sentence in its original form:

Quote:

Never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise.



Step 1. Make it a little less incomprehensible by adding some hyphens:

Quote:

Never imagine yourself not to be otherwise than what it might appear to others that what-you-were-or-might-have-been was not otherwise than what-you-had-been would have appeared to them to be otherwise.



Step 2. Turn double negatives into positives.

Quote:

Always imagine yourself to be what it might appear to others that what-you-were-or-might-have-been was not what-you-had-been.



Now the sentence can be rephrased into a rather dubious piece of advice, but one which follows logically from the moral the Duchess has reworded "more simply": "Be what you would seem to be" :

Quote:

Try to be the sum of others' impressions of you.



Does that make any sense?