If you're using ViewModels the best approach is to have two boolean properties (IsGridVisible and IsDropDownOpen) and two commands that change them (ShowCommand and HideCommand), this way you can control the visibility of the grid and if the DropDown is open or not.
I've attached a sample project that shows this so could you please examine it and if you have more questions feel free to ask.
p.s. If you're not using ViewModels you can manually change the IsOpen and the Visibility of the button and the grid in some click event handlers.
the Telerik team
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