Okay so I just got past this scene and I have an actual theory :
Marrow and Hamish are indeed Cole's biological dads
It wouldn't surprise me if Marrow really desired a son with Hamish, but since they're both males, he had to find another, unorthodox, method. He might have learned of the existence of a certain magic/spell that permits that and stole it from Agatha's lab
Thus, Cole was born. But maybe the disease he got during his childhood and leaving him weakened for the rest of his life was a result of his rather particular birth conditions.
Marrow might feel especially guilty, thinking it was because of him that his son ended up weak and not strong like him.
That would also be a reason why he despises magic so much (this and maybe something that happened with his sister)