The simmering divorce war between  Jennifer Lopez and Ben Affleck is threatening to explode into open hostility despite the estranged couple’s efforts to play nice for the sake of their kids, sources exclusively tell In Touch.

J. Lo, 55, and Ben, 52, were spotted having a tense exchange at the Beverly Hills Hotel during an outing with his kids Samuel, 12, and Fin, 15, and her 16-year-old twins, Max and Emme, on September 14. At one point, the This Is Me … Now songbird appeared to be wiping away a tear while Ben looked as stoic and steely-eyed as his Batman character.

“Jennifer would never make a scene in public, especially in front of their kids, but she has so much resentment,” spills an insider. “She’s made it plain she’ll never forgive Ben for being such a coldhearted jerk and giving up on the marriage in such a savage manner.”

Now, their uneasy truce seems to be strained to the breaking point. “She agreed to play nice and try to wrap things up without any fireworks,” explains the insider. “But the tension is palpable, especially when Ben rolls his eyes and refuses to accept any responsibility for the marriage’s failure.”

As In Touch’s readers know, the superstars quietly separated earlier this year, with Ben moving into a $100,000-a-month rental near the home of his ex Jennifer Garner. In July, he closed escrow on a $20 million French country-style house in Pacific Palisades, and Jennifer officially filed to end the stormy two-year marriage on August 20.

“Ben has made it crystal clear he’s not going back to J .Lo, and she’s fuming,” says the insider. “They were bickering behind the scenes even before this recent meet-up, which went about as badly as everyone feared.”

The source adds, “The sooner the ink’s dry on the divorce papers, the better it’ll be for everyone.”