Carly Rose Sonenclar's family is royally pissed off at LeAnn Rimes for -- as they put it -- trashing their daughter's "X Factor" performance Wednesday night.
Sources connected with the family tell us ... the 13-year-old girl's mother is livid that Rimes would dare say Carly Rose was "nervous and had trouble hitting the right notes" when she sang "How Do I Live."
As you know ... Carly Rose did a duet of the song with Rimes on the show. People on social media went crazy after the performance, claiming Rimes was drunk.
TMZ broke the story ... Rimes insists she was sober, but says if things were awkward, it was only because, "I was trying to help this 13-year-old girl who was having some trouble with the song." Rimes later claimed she never gave a quote, but we can tell you ... her rep specifically gave us the quote and told us we could use it.
Carly Rose's mother and other relatives are telling people they can't believe LeAnn threw their daughter under the bus, and that it was clear -- Carly Rose was a pro and even out-performed LeAnn at her own song.