Police threaten and intimidate people all the time. The courts even permit police to lie to witnesses and victims to try to elicit information out of them.
If you are saying that you gave a false police report -- but you did so only through police coercion, this is a very complicated situation. Both you and him could be convicted -- him, of domestic violence and you, of falsification, making a false report, etc.
Both of you need an experienced criminal defense attorney, but you probably cannot have the same attorney because they is a conflict of interest. You can testify that you agreed to a false police report, but only because the police were trying to blackmail you with your daughter, but the prosecutor could threaten you further with criminal charges.
Consult with an attorney in private as soon as possible.