First of all, I always think its praiseworthy to salute those who stand up for children and against the cowards who abuse children. It shouldn't have to be that way, but there are too many stories about adults who don't do that, and I think the good guys deserve their props.
I'd be curious how the custody arrangement was created. I think it a very wise first step to involve the authorities and to ensure that the child's health is cared for. Having done that, I would be thinking about legal processes to limit the father's custodial time with the child. It might cost some money and it may bring its own set of problems, but if there's proof that the father is abusing the child (and the do entation from last night will begin (and hopefully end) that process), it's perfectly valid to revisit custody from a legal standpoint. If the custody arrangement is created through a divorce decree, the trial court that signed the decree has continuing jurisdiction to revise the decree to change things like custody. If there is no mention of custody in the decree (or if there isn't any decree for some reason), either parent can seek to modify the custodial arrangement or to have a court declare the custodial rights of the parents. It will be harder to do, unfortunately, if there is only one incident and that incident could be understood to be a harder-than-normal spanking; but the welfare of the child should always been paramount and there are means of restricting custody that don't wholly eliminate the father's rights. It could be that the child could visit the father for a probationary period while requiring that the father always have another adult in the room or something creative like that. There are, I am sure, lesser sanctions than complete deprivation that will protect the child while respecting the father's rights (absent convincing proof of abuse) and any good family law attorney will know of an array of options that might prove to be useful in such a situation.