What about this Scenario ?
Nixon give George H.W. Bush the Job of NASA Administrator, (after loosing the election as Senator of Texas)
The Soviet manage to land Cosmonauts on Moon in 1971
Nixon is forced to continue the Space race by to revitalize the Apollo program (no Mars or Shuttle program)
Bush Senior restart production of Apollo Hardware and Saturn V production, including more Skylabs.
In mean time his son George W. Bush is pilot at the Texas Air National Guard. (under Air Force Reserve Command)
He file a application for Astronaut selection for NASA Group 8 (here in 1974 instead of 1978) and get selected.
This let later to G.W. Bush Astronaut controversy about how he could enter the Group 8, despite his poor record as Pilot under AFRC.
and if his father as Nasa Administrator was involved in this.
Bush junior manage quite well as CSM Pilot and become selected for Apollo Backup crews in 1970s
He get his first spaceflight with Apollo 23 mission in 1977
in mean time George H.W. Bush resign from Office, do dispute with president Udall administration, special with vice president Walter Mondale.
Bush Senior will return as Vice president under President Ronald Reagan (1911-1981)
Bush Junior fly several Apollo and Skylab mission, as mission commander on Apollo 27 the last apollo mission, bevor Moonlab program.
until his father become president in 1981.
NASA Administration use now George W. Bush as liaison Officer between NASA HQ and White House
Despite no more space flight, George W. Bush get the taste of Politics, He help on his father's campaign for reelection in 1984.
Supported His father on Space Exploration Initiative.
He resign from NASA in 1990 for Political career and won the election to Governor of Texas in 1994.
As "the Astronaut Governor" he supported NASA centers in Texas, and win the reelection as Governor in 1998
He won the 2000 United States presidential election, becoming the First President who was Astronaut and walk on the moon...