There are a ton of isues sharing the dataProvider between components. We've run into this with a lot of clients using our AutoCompleteComboBox.
You can easily use the same source, but a different--separate--collection for each of your dataProviders.
var dataProvider1 :ArrayCollection = new ArrayCollection(someArray);
var dataProvider2 :ArrayCollection = new ArrayCollection(someArray);
var dataProvider3 :ArrayCollection = new ArrayCollection(someArray);
Each collection is just a wrapper around the base source. Sorting one will not affect any of the others, leaving your other ComboBoxes or DropDownLists untouched.