From the description of the tasks that you are supposed to accomplish I came to the conclusion that the RadSplitter may not be the best control for the task and a better choice for this would be the RadPanelBar. Please, review the demos for the RadPanelBar control
and check, if that is actually the control that will provide easier implementation and richer functionality for the result that you wish to accomplish. Otherwise I will gladly help you with the issues that you are experiencing with the splitter, although it is not exactly designed for the tasks you will to complete.
Hope this helps.
All the best,
the Telerik team