You can use org.eclipse.ui.IWorkbenchPage.findView(String) to return the IViewPart (the instance of the contributed object that created that view). From there, you would have to know and have access to the class and internals to get ahold of their Tree object:
IViewPart part = workbench.getActiveWorkbenchWindow().getActivePage()
.findView(MyView.ID);
if (part instanceof MyView) {
MyView view = (MyView) part;
// now access whatever internals you can get to
}