My question is what are my rights when the landlord won't fix a mildew problems and my kids are getting sick and he still wants the rent without fixing the problem that he's known for about 4 months.

1) Always report in writing, dated, with a copy for yourself.
2) Take pictures
3) Never withhold rent unless you give it to a lawyer to hold in escrow.
4) Final resort, call the Health Dept.

If helps if you know the cause of the mildew. Bathrooms tend to mildew no matter what, just because of so much moisture from showers. Is there a window? Is there an exhaust fan?

There is no reason to shower with the door closed, or to keep the door closed when not using the toilet, especially if there are several of you taking showers.

Many states will allow a dissolution of a lease for "Health and Safety" reasons. Mildew may or may not be a valid reason unless you can show that is the direct cause of the children getting sick.