Here is a solution that I use with success to remove mildew from the exterior of a house: 2 tablespoons dish detergent
(Dawn, etc.)
2/3 cup Trisodium Phosphate (TSP)
1 quart bleach
3 quarts water
I mix the ingredients in a pump-up garden sprayer and apply to the affected area, let it do its work for a couple of minutes then spray the wall with a garden hose to rense off the solution. It works great. A commercially prepared solution which works well also, but costs a lot more is Jomax, mfd. by Zinsser (http://WWW.Zinsser.com)
Trim replacement is not necessary as long as there is no rot associated with the mildew. As long as the surface is properly prepared (mildew removed) a couple of coats of mildew resistant house paint should do the trick. Even if you don’t use their cleaner, I would recommend Zinsser paints for this.