The three plays in Preston Jones s A Texas Trilogy are

The three plays in Preston Jones’s “A Texas Trilogy” are completely independent, and each has only a peripheral relationship with the other.

(A) independent, and each has only a peripheral relationship with the other
(B) independent, and each has only a peripheral relationship one with another
(C) independent, and they have only a peripheral relationship with the others
(D) independent and have only a peripheral relationship with one another
(E) independent and have only a peripheral relationship each with the other

OK. Since we are talking about three plays, and three particular plays at that, we have to locate an option that leaves no ambiguity, and also removes the grammatical errors seen.
A: incorrect; three plays, and have only peripheral relationship with 'other'!!
B: Incorrect. The use of another means that each of the play has only a peripheral relationship with 'one other' play. Doesn't specify its relationship with the third play.
C: 'with the others' could mean any of the millions of plays written till now by all the playwrights.
D: Bingo! We use one-another to refer to more than two persons/ objects. So, each play is unique, and has only a peripheral relationship with the other two.
E: 'With the other' implies there are only two sentences involved.

Hope it helps. Cheers!