Your tree is infested with one of the insects that feed on the sap produced by the tree. These insects excrete sugary, sticky poop constantly. A side effect of the sweet 'honey dew' is the growth of a simple black mold, commonly called black sooty mold. Get rid of the insects and the black sooty mold will go away on its own.

If you would like us to help you, which we would be happy to do, we must have the identity of the trees and decent pictures of the 'little white spots '.

Possible culprits are scale insects, aphids, leaf hoppers.

"the leaves also have little white aphids on them and they have just started flying off the leaves. "

You may want to buy some ladybugs & lacewings, etc..

Or maybe plant different types of trees instead. Is it a citrus tree?

Here is a link that might be useful: Green Lacewing