The singer cheated on Dean Sheremet in 2009 when she met and fell in love with Cibrian, who then separated from his wife Brandi Glanville in order to be with Rimes.
The couple wed last year and the Grammy winner admits the media backlash was hard to deal with.
In an interview with Katie Couric, which will air on Friday, she says, "It was very, very difficult. I wouldn't wish it on anyone and especially in the public eye to go through all of it."
And, as a way to deal with her feelings of remorse, she's poured her emotions into a song called "What Have I Done," which will be released on her new record Spitfire and Rimes admits she can't wait to let go of the weight she's been carrying around since the cheating scandal.
She continues, "I've carried a lot of guilt for a long time, I think."
Rimes reveals she has also penned a tune, titled Borrowed, which also chronicles her film set romance with a married man.
She adds, "I carried the title around with me for about eight months, because I was so unsure of how to write it, without offending anyone, because I had to be so honest in order to write it."
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