Divorce and custody are heard in two different courts here
New York splits what most states keep in one place, so a lot of the confusion your audience carries is about which building they belong in.
A divorce and a custody or support petition do not begin in the same court in this state, and somebody saying they are going to family court is often describing a matter that starts somewhere else entirely. The words do not mean what a national video says they mean.
So publish the map. Which kinds of matters begin where, what each court is usually called in ordinary conversation, and which one a person is describing when they use the phrase everybody uses.
The borough changes the address on top of that, because each one is its own county. A viewer in Forest Hills and a viewer in Park Slope are not walking into the same building for the same kind of case, and saying so saves somebody a wasted morning and a lost day of work.
Keep it procedural and stop before the advice. Where a matter is heard, what a first appearance generally involves and what to bring are useful and safely general. What will happen in one particular case is not.