Been there, done that with the whole "mold" testing and remediation thing - I'm in Florida also. From speaking with Department of Health representives in Tallahasse to conversing online with Industrial Hygienists I learned a ton about it. Overall, the whole thing is a way overblown to the point it nears scam territory. In the middle of the stress you are already undergoing this is something you don't really need to be starting a crusade over.
The entire industry has been going crazy making a lot of money on our fears. In FL, take a 14 hour course and pay about $100/ year for a license and you too can become a licensed "mold assessor" and "remediator". Mold is naturally occuring and exists everywhere, especially in Florida. Are your kids in danger every time they walk outside and are they falling sick all the time? Probably not, and even in the slim chance they are - get a $150 allergy skin test to confirm it's even allergies making them sick. Which is something a $8 bottle of Fluonase can fix.
If she doesn't have an active water intrusion and is running the AC, she is not going to have an active mold infestation in the house. It needs water and dark.
Do not waste your money on a "mold test". All they do is collect a bunch of spores in a dish, which you mail in to a lab and a guy making a couple bucks an hour counts the spores and sends you a fancy computer generated report about how many there are. Mold is naturally occuring - of course there will be spores in the air. Over the course of the day spore count can vary considerablly and tons of factors account for variation - was a window or door left open, was it night or day, where was the testing kit placed in the house, were there a lot of people and pets in the house. There are no standards or baselines for these reports so they are useless. It's very simple, if you can see it and smell it you have mold and that still doesn't necessarily mean anything in terms of your health. You don't need to spend money to figure it out. Use common sense.
And for godsakes do not pay for "professional" remediation or duct cleaning unless you like flushing thousands of dollars down the toilet. Unless drywall, floorboards and carpet are completely rotted out from water damage, there is no need to bring in a hazmat team to tear everything out. "remediation" is as simple as stopping the leak, putting on a one dollar face mask and cleaning up the mold with a damp rag and some elbow grease.
Hopefully the mother of your kids will use some common sense. If the house smelled like manure, you'd think she would take care of it. I'd expect the same in this situation. The fact that your kids' friends won't even come to the house anymore, would lead most people to do some cleaning.