Your first plan of attack:
When you want to remove mildew stains, reach for white vinegar first. It can be safely used without additional ventilation and can be applied to almost any surface: bathroom fixtures and tile, clothing, furniture, painted surfaces, plastic curtains, and more. To eliminate heavy mildew accumulations, use it full strength. For light stains, dilute it with an equal amount of water. You can also prevent mildew from forming on the bottoms of rugs and carpeting by misting the backs with full-strength white vinegar from a spray bottle. Plus, there are over 90 vinegar uses (white or apple cider vinegar) that can clean a lot more than just mildew.
To clean furniture:
Ammonia is what you need. Clean the mildew off unfinished wooden patio furniture and picnic tables with a mixture of 1 cup ammonia, 1/2 cup vinegar, 1/4 cup baking soda, and 1 gallon of water. Rinse off thoroughly and use an old terry-cloth towel to absorb excess moisture. (This same combination can clean painted outdoor surfaces.) To remove mildew from wicker furniture, wash it down with a solution of 2 tablespoons ammonia in 1 gallon of water. Use an old toothbrush to get into hard-to-reach twists and turns. Rinse well and let air-dry. An important safety note before you use ammonia in any part of your home: Be sure you use it in a well-ventilated area, always wear rubber gloves, and never combine ammonia and bleach.