One prominent Senator whose son did serve in Vietnam was the powerful Al Gore Sr. (D-TN), but the favoritism shown to his son, the future Vice President Al Gore, is still reflective of the treatment scions of powerful families could expect.

Al Gore Sr was a relative liberal by Southern Democratic standards, much like his Tennessee colleague Estes Kefauver: early in his Senate career he was one of only 3 of the 22 Southern Democratic Senators to refuse to sign Strom Thurmond's Southern Manifesto, a notoriously uncompromising defense of white supremacy. Gore voted against the Civil Rights Act of 1964, but did break with other Southerners to vote for the Voting Rights Act of 1965. Gore was an enthusiastic supporter of LBJ's domestic agenda, especially Medicare, but was a critic of the Vietnam War. With reelection coming up in 1970 and a hawkish public back home in Tennessee, it would've been political suicide if Gore's son, who had just graduated from Harvard, skipped the war.

Al Gore campaigned for reelection with pictures of his son in uniform but still lost narrowly in 1970. Two months later, in January of 1971, Al Gore Jr. shipped off to Vietnam. However, once there, Gore wasn't exactly on the front lines. Gore worked on the Castle Courier, the newspaper of the Army Corps of Engineers, a relatively safe posting that kept him out of harms way for the 5 months he spent in Vietnam. At the end of May, 1971, Gore returned to the U.S. no worse for wear.

I'm posting this story because you're going to be inundated with stories of the sons of the powerful avoiding Vietnam altogether. Al Gore Jr.'s five month stint as an Army journalist is a nice view as to what happened to those powerful people who actually did serve.