The former couple - who split in July after seven years of marriage - had agreed an amicable arrangement where the 'American Idol' judge was primary carer of three-year-old Max and Emme, but the Latin singer is now said to be seeking joint custody.
Sources claim Marc "hit the roof" when he saw pictures of Jennifer's new boyfriend Casper Smart bonding with the youngsters.
The insider added to the new issue of Us Weekly magazine: "It caused a huge blow-up.
"[Now he is] going back on his word and saying his wants joint custody."
Those close to the situation insist Marc's motivation to take action is to make the 'On the Floor' hitmaker "suffer" because he is angry she has found love again.
The source said: "He wants to make Jennifer suffer because she's having fun with someone new, and he knows this will hurt her on the deepest level."
However, the singer-and-actress is not prepared to give in to her estranged spouse and is ready to fight him to keep the custody arrangements as they are.