Hi James.
I think you can do it by using the TableDescriptor.VisibleColumns.IndexOf("ColumnName") property.
So, for instance if you want to move column "ProductName" position to "ProductDescription" position, you can achieve it through the following statement:
gridGroupingControl1.TableDescriptor.Columns.Move(gridGroupingControl1.TableDescriptor.VisibleColumns.IndexOf("ProductName"), gridGroupingControl1.TableDescriptor.VisibleColumns.IndexOf("ProductDescription"));