You can't nest divisions, leagues or teams because, the type of the children collection of the drop target node doesn't match the type of the dragged node. To make it clear, lets take the Division object for example. It have a children collection of type Team. When you drag another Division object and try to drop it in the Division under the mouse, the treeview cannot find a children collection of type (Division) and the drop operation fails.
In order to achieve your requirement you can create a base class and base each node type on it. Then in each node class add a collection of the base class.
However, using this approach you will need to change the data templating approach. Now you will need to use implicit templates or a data template selector. You can see this demonstrated in the attached project. Additionally, you can take a look at the Drag and Drop help article
in the RadTreeView help documentation.
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