I'm not sure if this particular incident is about that but there is a notable one where Engels writes to Marx informing him about his wife's death and Marx in his response asks Engels for money which upsets him a little bit which he makes known in his following response.
i just wnated to nitpick that Engels was never married to Mary Burns. However, he was married to Lizzie Burns, Mary's younger sister. He only married Lizzie on her deathbed, about an hour before she died.
Engels was a bit of a womanizer, like he slept with Sibylle Hess, who was the wife of a guy he hated Moses Hess. I'm personally of the opinion he's the one who got Helene Demuth pregnant, the Marx family's housekeeper.