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It is possible to redefine the DatePicker's template and add some additional button for your case, but you will have to write a lot of XAML code in order to achieve the same UI of the control. We have a post on
how you can do this using Expression Blend. Another problem is that you have to add custom logic for handling the button click event, of which RadDatePicker will not be aware. I think that your suggestion (Creating a separate UserControl which consist of a RadDatePicker and a button) is the easiest way to accomplish your task.
the Telerik team