DISGRACED politico JOHN EDWARDS is going to be a grandfather, but the happy news has triggered an ugly family feud!

Edwards’ pregnant daughter Cate, 30, wants to name her baby after her late mother Elizabeth if it’s a girl, and she won’t allow her father’s girlfriend Rielle Hunter anywhere near the child, says a source.

“Cate sternly reminded John of all the hell that he and Rielle put her poor sick mother through before she died,” noted the source.

“Cate made John relive his shame and he was totally demoralized. The joy of becoming a grandfather was very short-lived.”

AS THE ENQUIRER HAS REPORTED, the former North Carolina senator and presidential candidate, 59, recently moved his ex-mistress Rielle, 48, and their love child Quinn, 4, closer to the Chapel Hill estate that he shares with daughter Emma Claire, 14, and son Jack, 12.

Cate married physician Trevor Upham in 2011, after her mother lost her brave battle with breast cancer at age 61 in 2010.

Their baby is due this summer, and if it’s a boy, Cate will name him after her brother Wade, who died in a car accident in 1996, said the source.

“Cate is hoping this new chapter in her life will honor her family, specifically her mom and brother, and not her father’s tarnished legacy,” added the source.

“And John knows if he does anything more to embarrass the family, Cate may make her baby off-limits not only to Rielle, but to him as well!”