OK. So to accomplish this, you have to build and use an ESRI Custom Tool. Here's what I did...On the DockableWindow button's On_Click method, i reference a Custom ESRI Tool that I created.
private void button1_Click(object sender, EventArgs e) {
IApplication app = Hook as IApplication;
UseCustomToolOnWindowsForm(app, @"Dharma_Inst_CustomUIElements_FindFeaturesFromPoint");
}
.....
<<Insert the following ESRI Snippet>>
public void UseCustomToolOnWindowsForm(IApplication application, System.String uidValue){...}