There's 3 scenarios i think the mom plot could develop
1) she's really a scumbag
2) she only divorced, but the kid got It wrong and he didnt want to see her anymore
3) she's an assassin and thinks only the daughter can live with her (and maybe train)
So Far i think its 3, because the daughter Said that the mother would not accept an assassin with his son, so she cares about him at least to a certain level and she cared about him in his infancy, it seems, but at the same time the kid got traumatized too much to be a judgement mistake, so its likely the mom really abbandoned him.
With this contradiction, It seems she believed she had to leave her family because of that dangerous life and blablabla that classic trope. I also think that either the father or mother have some kind of relationship with the mysterious sick man, and thats How he knew the kid and How he changed an assassin heart.
I Hope its not 3 its too lame, and i dont like 1 for this story, because Its contradictory she liked the kid and still cares about him (a little at least) so It would be a weird development to despise the kid suddenly and only care about the daughter.
I would Hope its 2, the kid is kinda dumb so Its not Impossible.