If you have a lawyer representing you whether in Supreme Court or Family Court, most of the time (unless you are testifying) you should let your lawyer do all of the talking.
There are many reasons for this which include your lawyer best knows how to present your position and respond to the judge. The statements that your lawyer makes are "argument" and cannot be used directly against you because they are not your statements. Your lawyer may have a good working relationship with the judge and knows what words and arguments are most likely to get the judge's attention. Your lawyer may be better at deflecting an unwelcome comment or question. Your lawyer may be better able to "spin" because they know the "buzzwords".
More often than not if the client tries to speak (unless the judge has asked the person a direct question) the judge will warn the client that they have a lawyer and should let their lawyer speak for them. If the client has a lot to tell the lawyer, a brief recess can even be requested. Sometimes, the client may not fully understand the purpose of the conference and if they start to speak they bring up matters that either are not needed for that appearance or they may actually open a can of worms.
Obviously, a person who does not have counsel has no choice and must advocate their position as nobody else will do so. If there are children involved, both the lawyer or the unrepresented client must pay attention to the oral report of the child's attorney. There is usually a lot of useful information whether favorable or unfavorable to be learned.
If you do speak to the judge always be respectful. Do not get angry as the judge does not have a personal vendetta against either person. That does not mean to say that the judge likes what someone may or may not be doing, but it is not personal. First impressions are critical. Subsequent impressions may cement the first impressions. Try to appear reasonable. Do not raise your voice. Do not act like the judge is not trying to help resolve your case. Lawsuits often do not move at the speed that people may need, but that is because of the volume of cases and the court's assessment of how urgent your case is and whether it needs more attention as in an earlier date to return to court. If the judge asks a question answer it directly. Judges know when people are evasive with sudden memory lapses or lacking basic information.
The above advice is useful in contested divorce cases, child support determinations, custody matters, property division and orders of protection. In other words the advice is universal.