Under California Family Code §3027.1, false allegations of child abuse or neglect that are made during a child custody proceeding can be subject to sanctions. The judge would decide whether to impose any or not, after you make a motion to request sanctions. A show cause hearing will be scheduled, to allow your ex the opportunity to show why sanctions should not be imposed.
If you do not file any motion, you can still challenge any untrue statements made by your ex, so the judge is aware that what she is saying is false and unsupported by evidence. You should not, however, make any statement that could be used against you. Point out the erroneous statements made by your ex to the court, but otherwise remain silent on the false allegations.
It is actually rare for a judge to find a party in a divorce or custody hearing in contempt of court. But if your judge feels that your ex is making his job difficult, trying to sort out the lies from the truth, and if he finds the lies she is telling especially heinous (as false allegations of child abuse are), he could impose a fine, or potentially jail her.
A doctor is a mandated reporter. He must report all cases of suspected child abuse. The suspected abuse is then investigated. If you were not contacted about an investigation, the investigator (if any) did not find your ex's allegations sufficiently believable to warrant an investigation.
But, yes, you are correct that if someone takes a child to a doctor and the doctor sees an injury that is consistent with abuse, he must make a report of the injury so the cause can be investigated.