1) Children still drive their parents' cars before they have achieved legal age, though judge's rule that they ought to be hold in contempt of court — Incorrect. “Judge’s rule” is a noun. What the sentence intends is for the “judge or judges” to be the subject and “rule” to be the verb. The possessive is changing the meaning here. From describing that “judges may rule to hold those kids in contempt” to “rule of judge”. Subtle change in meaning. Eliminate.
2) Children still drive their parents' cars before they have achieved legal age, though it is ruled by judges that they ought to be held in contempt of court — “it is ruled by judges that..” the passive construction isn’t really needed here. Keep but not very convincing.
3) Driving their parents' cars before children have achieved legal age, though held in contempt of court, rule judges — who is driving? Modifier error. Eliminate.
4) Children still drive their parents' cars before they have achieved legal age, though judges rule that they ought to be held in contempt of court — Correct. Fixes the error in B.
5) If children still drive their parents' cars before they have achieved legal age, judge's may rule that they ought to be held in contempt of court — same error as in A. How can “may rule” be a possessive of “judge”? Eliminate.
One comment here. “It” used in B is not lacking a pronoun. It is a placeholder pronoun. The worse error in B is usage of passive voice.
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