Complex sentence: In 1950, Gahagan Douglas ran for the United States Senate against Democratic incumbent Sheridan Downey whom she defeated in the primary, and Republican Congressman Richard Nixon, in a race that her supporters considered a prototypical smear campaign.
Split into simpler sentences: In 1950, Gahagan Douglas ran for the United States Senate to succeed Democratic incumbent Sheridan Downey. In the general election, she faced Republican Congressman Richard Nixon in a race that her supporters considered a prototypical smear campaign.