Of the two sentences, which one is correct: My mother, for whom I have an enormous respect for, is caring. or My mother, for whom I have an...

I think that this is an interesting question. You actually
have done better than most students.  I always find it easier to pare down student
writing as opposed to adding in.  For this particular question, all you have to do is
pare down and you are set.

In terms of what you have, you
should also be commended for not wanting to end a sentence with a preposition.  Students
have a tough time grasping this because of the gap between speaking and writing.  When
we speak, it's easier to end sentences with prepositions.  For example, "Whom did you
vote for?" is easier to say than "For whom did you vote?"  The first one is more
accepted as spoken English, while the second one, albeit grammatically correct might
sound more foreign to say.

In your particular question,
this is where you are.  Both sentences place the preposition "for" accurately in terms
of going before "whom."  Yet, since it's already in the sentence, one does not need it
again.  The first sentences has it twice, once in front of "whom" and then after
respect.  Since its placement in front of "whom" has already established its present, it
is not needed again.  Accordingly, the second sentence is correct because it only uses
the preposition once.