Apologies to you NP. The Anti-Nepotism Act was passed in 1967 post Bobby Kennedy.
I dug up the text of the Act. Here's the operative paragraph. (5 USC Sec. 3110)
b) A public official may not appoint, employ, promote, advance, or advocate for appointment, employment, promotion, or advancement, in or to a civilian position in the agency in which he is serving or over which he exercises jurisdiction or control any individual who is a relative of the public official. An individual may not be appointed, employed, promoted, or advanced in or to a civilian position in an agency if such appointment, employment, promotion, or advancement has been advocated by a public official, serving in or exercising jurisdiction or control over the agency, who is a relative of the individual.
Note the term "appoint", and no exception is made for the office of Vice President. One might argue that the term "nominate" isn't there, but that could be construed as advocating for employment. The President IS covered by this law (exceprt from paragraph A)..
(2) "public official" means an officer (including the President and a Member of Congress)...
And yes, since I know you're all dying to read
more of this scintillating prose, here's the link.
Document on uscode.house.gov (lengthy URL)
So, in short, no, the President cannot nominate his brother as Vice President. The Anti-Nepotism Act is the law, and it conflicts with nothing in the 25th Amendment or anywhere else in the Constitution.
Thanks! I knew that I was right, but my HTML skills are almost nonexistent, so I couldn't post that.