I have heard that theory before that R killed Bae’s mother (based on his long hesitation before responding to Bae’s question — “she is dead.”), but I don’t get that at all. There is certainly regret there. And possibly shame, possibly R feeling responsible for her death for some reason. But I don’t get any vibe that he killed her. Just that the whole subject is painful for him, maybe just because he is grieving the loss of his wife, or maybe because the soldier was truthful and she did leave him because his behavior disgraced her.
Here is something I just thought of —- if that is true and the mother left, why wouldn’t she take the boy with her? Was she just a b**** who didn’t care about her son? Did she hate the boy too because she thought he would turn out just like his father? Or (and this is the one possible scenario where I could see R murdering her) did she try to leave with the boy and R couldn’t bear to lose his son and so killed her. I could imagine that happening.
As far as R being a coward they certainly drove that point home over and over, but I would like to see the circumstances of R’s supposed cowardice in battle. He did tell Bae he had no choice. Personally, if faced with a horde of angry ogres I think I would run too!