Judge Bonham denied a motion
to allow members of the jury to go home at the end of each day instead of to confine them to a hotel.
The purpose of the motion (legal request) was "to allow the members of the jury to go home rather than [to] be confined to a hotel." The use of "to" after rather than is optional.
Here we are comparing "to allow" vs "be confined."
(A) to allow members of the jury to go home at the end of each day instead of to confine them to - after "of" preposition we need noun. Wrong.
(B) that would have allowed members of the jury to go home at the end of each day instead of confined to - "would have allowed" is a past perfect conditional used for hypothetical but there is not hypothetical here. "would have allowed" is not parallel to "confined to" because one is a verb and another a verbal (without any helping verb).
(C) under which members of the jury are allowed to go home at the end of each day instead of confining them in - correct idiom is "confining them to."
(D) that would allow members of the jury to go home at the end of each day rather than confinement in - "would allow" as a verb is not parallel to noun "confinement in." Also the correct idiom is "confine to."
(E) to allow members of the jury to go home at the end of each day rather than be confined to - "to allow" is parallel to "[to] be confined to"