The next release of OpenInsight includes a new TABCONTROL property called ALLOWDRAGREORDER, which allows you to drag a tab to a new position within the control. It's a simple boolean property, and when set to True tabs may be dragged and reordered with the mouse - an image of the tab is moved with the cursor, and a pair of arrows are displayed to mark the potential insertion point.
Here's an example of a tab being dragged in the IDE: