"Several misconceptions, common during World War II and after, continue to circulate about the Sullivan brothers and the assignment of family members to U.S. Navy ships.
Reference to a "Sullivan Act" in connection with family members serving in the same ship/unit is a popular misconception. The Sullivan Law of 25 May 1911 is a New York City ordinance dealing with firearms. Although proposed after the death of the five Sullivan Brothers, no "Sullivan Act" was ever enacted by Congress related to family members serving together. Similarly, no President has ever issued any executive order forbidding assignment of family members to the same ship/unit."
From the same source, Navy policy as of 1944:
"Bureau of Naval Personnel Circular Letter 345-44, 15 November 1944; Sole-survivor policySole Survivor Policy [Source: Navy Department Bulletin All Ships and Stations Letters, January-June 1945 (Still in effect 30 June 1945), Navy Department, World War II Command File, Operational Archives Branch, Naval Historical Center, Washigton, D.C.]
BuPers [Bureau of Naval Personnel]
CIRCULAR LETTER NO. 345-44 44-1285--Return to the United States of Sons of War-Depleted Families Pers -10D -JK, P16-3/00, 15 November 1944
ACTION: ALL SHIPS AND STATIONS
1. In recognition of the sacrifice and contribution made by a family which has lost two or more sons who were members of the armed forces and has only one surviving, and he is serving in the Navy, Marine Corps, or Coast Guard, consideration will be given to his return to, or retention in, the continental limits of the United States, except when he is engaged in nonhazardous duties overseas.
2. Applications for return to, or retention in, the continental limits of the United States must be filed by the serviceman himself or his immediate family. Request from the individual concerned shall be submitted officially to the Bureau of Naval Personnel for naval personnel, Commandant of the U. S. Marine Corps for Marine Corps personnel, and Commandant of the U. S. Coast Guard for Coast Guard personnel by their commanding officers. Applications received from immediate families shall be referred to the Bureau of Naval Personnel, Commandant of the U. S. Marine Corps, or Commandant of the U. S. Coast Guard, as appropriate.-BuPers. L. E. Denfeld."
Cursory research didn't provide much re Army policy. My guess would be that they may have had something similar to the Navy. I doubt that a demand for a non-combat position by the second son to whom you alluded would have carried any weight. If anything, it would probably have been regarded as a "request", since he undoubtedly had no standing to "demand". As I indicate, except for the Navy info set out above, this is strictly speculation on my part.