If he cannot function as an adult, then yes, AFAIK, DCF can intervene. Especially if his care is being provided by the state, they are responsible for ensuring his well-being. And if the problems are not corrected, they have the power to remove your brother from your mother's care.
How bad is the mobile home? Is it a cleanliness issue or a safety issue? What are the responsibilites of the caregiver? Is she solely to care for your brother's personal needs or does she have other responsibilities?
I'm sure someone will be along who knows FL law better than I. But I would take DCF seriously.