The couple – who have twins Max and Emme, three - separated after seven-years of marriage earlier this year and Lopez, 42, has since moved on with 24-year-old dancer Casper Smart.
But according to Us Weekly, Anthony is less than impressed with her new romance and 'hit the roof' when he saw pictures of Casper holidaying with J.Lo and their twins over Thanksgiving in Hawaii.
'It caused a huge blow up,' said the source, who added that while it has been agreed that Jennifer will have primary custody of the kids, he may go 'back on his word'.
'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,' said the insider.
But another source said the Love Don't Cost a Thing singer is 'ready to smash him if he tries anything… It's getting vicious.'