I know first hand that in Florida the fairness of a civil/family hearing depends a lot on the judge that is assigned to the case.
Florida law mandates that a general master makes the initial decision for the immediate residential custody status of the minor child(ren) and calculates child support. In cases where the child's best interests are not being met...the court may appoint a Guardian Ad Litem.
Florida law also mandates that the parties mediate to try to resolve their differences prior to going to trial. This is a step in the right direction but considering the fact that couples separate because they don't get along...initial mediation sessions don't produce much more that a framework for the attorneys to know what their dealing with. Mediation is private and the discussion is not admissible in court; only the agreement is.
If in the disclosure process allegations of abuse arise the court may order psychological evaluation of the parents and children.
A decent psyche eval from a reputable doctor can run around $5,000 to $10,000 dollars.
In cases with allegations of abuse the burden of proof is on the accuser. Some judges I've gone in front of take these allegations seriously and, as the law demands, require the plaintiff to substantiate their claims of abuse ie. ER records, family doctor reports, documentation from teachers, psyche eval reports, etc.
If a spouse/parent fails to report spouse abuse/child abuse they will find they have no credence in front of a judge in the future.
As soon as an instance of physical/sexual abuse occurs it is imperative the adult victim or the child's parent report it. I cannot stress enough that if these acts go unreported then the wronged parties have little recourse in a court of law.