Dear A___:

You wrote:

>a. I didn’t tell it to my mother and neither to my father.
>b. I didn’t tell it to my mother and nor to my father.
>c. I didn’t tell it to my mother, neither to my father.
>d. I didn’t tell it to my mother, nor to my father.

>Which of the above sentences are acceptable?

They all have problems.
B is awful, two conjunctions in a row? (“And nor”)
A is understandable, but a native speaker would say “and not to my father either,” if he used “and.”
C is understandable, but you would seldom hear a native speaker say it because of the double negative.
D is also understandable, but normally one would say “or to my father” since the verb is modified by “not.” It is another double negative.

Better than any of the above:
I didn’t tell it to my mother or my father.
I didn’t tell it to either my mother or my father.
(The second “to” in both sentences is optional.)

It you wanted to use “neither” rather than “not,” you could say:
I told neither my mother nor my father.