Well if you are talking about a custody or divorce trial the answer is yes and no. The rules of evidence don't allow for hearsay unless it fits into one of the hearsay exceptions. In addition, if you fear they will bring in things that are less reliable you should file a Rule 2B notice at least 45 days prior to the trial. This means that you are alerting the other party and the court that you want the rules of evidence strictly applied. This will make it harder(for both sides) to use evidence that does not conform to the rules. Be careful; it applies to you too.
You would want to file a Rule 2b motion, that calls for a strict following of the Arizona Rules of Evidence. You have to do this at least 45 days prior to the hearing. See the link to my legal guide below that discusses the Rule.