I believe you're looking for him to sign a "Consent to Travel" form to allow you to take your daughter across the border, right? I think there's some confusion here as to whether your looking for him to consent to a PR.
My wife has joint custody of her daughter with her biological father (I am the step-father). As I am American and they are all Canadian, my wife has stipulated in the divorce agreement that her daughter's biological father would sign the consent to travel form for normal travel. So, he is obligated by the courts to do so. That being said, the US Border Services agent at the gate has never asked her to provide the consent to travel form (she has travelled across with her daughter about 5 times).
I would proceed with caution, however. I understand your frustration with your daughter's biological father, but I would strongly suggest proceeding through legal means to establish sole custody of your daughter or work out an agreement for him to consent to travel abroad. If you are trying to remove her from a bad situation by taking her out of the country (as indicated by your responses), I can understand her father's reluctance to sign that consent. In that case, her father can take pre-emptive actions that could make things a lot more difficult for the both of you.