I am not quite sure I understand the collapse / expand question. What to you mean by splitter to collapse / expand itself? RadSplitter is a content container control that splits the page in different sections(panes) that can be collapsed / expanded.
Regarding the GoogleMaps API v3, there should not be a problem using it on the page together with RadControls. I tried to incorporate it in a sample page with RadSplitter and the control and the map are working as expected. For your convenience I have attached a my sample test page.
the Telerik team
If you want to get updates on new releases, tips and tricks and sneak peeks at our product labs directly from the developers working on the RadControls for ASP.NET AJAX, subscribe to their blog feed