I don't do mold but...

I thought I would share, this air handler is running and there are children living in the home.

No need for any testing there. I would say that they definitely have a problem.

That is bad news! You would no doubt find mold inside air handler, in duct work, and any damp areas of home.
Did you notice mold spots on interior of metal window frames?
Bet if you ask they will tell you they have a hard time keeping bathroom clean. It will even start to grow on toilet bowls in a matter of days with that much constant flow of fresh mold.

You misunderstand mold, Ed. Mold on hard surfaces seldom test considered toxic. Consider toxic molds got to have something to eat on such as in this case, paint and wood.

When there is a constant source of new mold spores coming from an air handler it will be found growing or attempting to grow on all indoor surfaces that have even a small amount of moisture. Bath towels, kitchen towels, your shower etc. It will continue to come back (indoors) as fast as you can clean it because there is a constant new source.
It may not kill you, but in large quantities it is all an irritant
Cure the problem at the air handler and you cure the rest of the problems.

Here is one from today. This is what happens when you do not clean the condensate line and ignore the problem.