Thank you! I believe I tried that in the 9.3 environment and got the managed execution error. However... since originally posting this question I have updated to v10 and am using the add-in framework. IDockableWindow.Show works fine. Here is the code:
' Close dockable window when OK button is clicked
Private Sub cmdOK_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles cmdOK.Click
Dim dockWinID As UID = New UIDClass()
dockWinID.Value = My.ThisAddIn.IDs.frmAOIInfo
Dim dockWindow As ESRI.ArcGIS.Framework.IDockableWindow = My.ArcMap.DockableWindowManager.GetDockableWindow(dockWinID)
dockWindow.Show(False)
End Sub