Hello, well since the question was not qualified in requesting women politicians involved in sex scandals to the US alone. I can name one.
Edwina Curry. Edwina Curry was a junior minister in the Thatcher Administration in Britain in the early 1980's, she was sacked after declaring eggs unsafe due to Salmonella.
She languished on the government back benches until John Major became Prime Minister in 1990. Soon after Edwina was promoted to a ministerial post. Only to resign after a couple of years on the release of the story that she had been having a long time affair with John Major.
Both were married to other partners throughout the affair. In Britain the affair was a shocker, but her political career was smashed to pieces, John Major however seemed to gain some kudos as he had been presented by the media as a grey man, no personality, no policies, no drive, hardly a blip on the radar screen of history, now HE had an affair! What a dog!