CHER made a vulgar slap at SARAH PALIN that’s sparked World War III with the outspoken diva’s two kids!

In an explosive message on Twitter, Cher sniped that the former Alaska governor’s picture could be found in the dictionary “under dumb c word.”

The singer’s son Elijah Blue Allman was so appalled that he posted an apology for his mom’s “ugly remarks” on Twitter, a source says, but then Cher blew up!

“Elijah thought his mom’s comments were classless and took it upon himself to issue an apology,” a source told The ENQUIRER. “But when Cher found out, she immediately called Elijah and lashed out at him.”

To make matters worse, Cher dragged her transgender

son Chaz, 44, into the fight, thinking he’d take her side, according to the source.

“But Chaz ended up telling Cher and Elijah that they were both wrong,” said the source. “Now, the three of them are fighting like cats and dogs – and it looks like there’s no end in sight!”

It’s not the first spat between the 67-year-old star and her kids.

As The ENQUIRER REPORTED, Cher and Elijah, 37, clashed over his then-fiancée’s involvement in the controversial Children of God religious sex cult. And Cher’s oft-stormy relationship with Chaz has recently been strained over her disparaging remarks about Chaz’s late father, Sonny Bono.

“Cher knew she was going to take some heat from Sarah Palin’s supporters for blasting her on Twitter,” said the source. “But she never imagined that she’d have fallout from her own children!”