klekota, I am also a Canadian. I raised my family in Canada, (although I now live in the US). I know of SEVERAL cases where Canadian fathers got custody of their children when the mother was unfit. One was a case of a woman I worked with losing custody of her daughter to the father. In that case, the mother was "just" drinking too much but never physically abusing the child.. however the father still got custody because an intoxicated or passed out mother is indeed a negligent and unfit parent! Your case involves physical , verbal and emotional abuse, I can not see a sane authority not seeing reason.
I hope you get good advice from the abuse hotline. I hope they give you some solid resources to pursue. Please let us know what they say. Your answers could help someone else in your situation.
Of course I don't know where in Canada you are or if you have Indigenous ancestry, but often times their are resources available through various First Nation groups.