Run the attached application.
Select datepicker from the dropdown.
click button to replace the skin.
In constructor call of the DatePickerSkin class there is an exception:

But I don't see such exceptions for ColorPicker or ComboBox

Exception in thread "JavaFX Application Thread" java.lang.IllegalStateException: Exception on contructor call.
at javaapplication36.ControlsSkinsApp$ControlsSkinsScene$1.handle(ControlsSkinsApp.java:83)
at javaapplication36.ControlsSkinsApp$ControlsSkinsScene$1.handle(ControlsSkinsApp.java:63)
at com.sun.javafx.event.CompositeEventHandler.dispatchBubblingEvent(CompositeEventHandler.java:86)
at com.sun.javafx.event.EventHandlerManager.dispatchBubblingEvent(EventHandlerManager.java:238)
at com.sun.javafx.event.EventHandlerManager.dispatchBubblingEvent(EventHandlerManager.java:191)
at com.sun.javafx.event.CompositeEventDispatcher.dispatchBubblingEvent(CompositeEventDispatcher.java:59)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:58)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:114)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:56)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:114)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:56)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:114)
at com.sun.javafx.event.EventUtil.fireEventImpl(EventUtil.java:74)
at com.sun.javafx.event.EventUtil.fireEvent(EventUtil.java:49)
at javafx.event.Event.fireEvent(Event.java:203)
at javafx.scene.Node.fireEvent(Node.java:8096)
at javafx.scene.control.Button.fire(Button.java:185)
at com.sun.javafx.scene.control.behavior.ButtonBehavior.mouseReleased(ButtonBehavior.java:182)
at com.sun.javafx.scene.control.skin.BehaviorSkinBase$1.handle(BehaviorSkinBase.java:96)
at com.sun.javafx.scene.control.skin.BehaviorSkinBase$1.handle(BehaviorSkinBase.java:89)
at com.sun.javafx.event.CompositeEventHandler$NormalEventHandlerRecord.handleBubblingEvent(CompositeEventHandler.java:218)
at com.sun.javafx.event.CompositeEventHandler.dispatchBubblingEvent(CompositeEventHandler.java:80)
at com.sun.javafx.event.EventHandlerManager.dispatchBubblingEvent(EventHandlerManager.java:238)
at com.sun.javafx.event.EventHandlerManager.dispatchBubblingEvent(EventHandlerManager.java:191)
at com.sun.javafx.event.CompositeEventDispatcher.dispatchBubblingEvent(CompositeEventDispatcher.java:59)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:58)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:114)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:56)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:114)
at com.sun.javafx.event.BasicEventDispatcher.dispatchEvent(BasicEventDispatcher.java:56)
at com.sun.javafx.event.EventDispatchChainImpl.dispatchEvent(EventDispatchChainImpl.java:114)
at com.sun.javafx.event.EventUtil.fireEventImpl(EventUtil.java:74)
at com.sun.javafx.event.EventUtil.fireEvent(EventUtil.java:54)
at javafx.event.Event.fireEvent(Event.java:203)
at javafx.scene.Scene$MouseHandler.process(Scene.java:3621)
at javafx.scene.Scene$MouseHandler.process(Scene.java:3391)
at javafx.scene.Scene$MouseHandler.access$1800(Scene.java:3342)
at javafx.scene.Scene.impl_processMouseEvent(Scene.java:1626)
at javafx.scene.Scene$ScenePeerListener.mouseEvent(Scene.java:2401)
at com.sun.javafx.tk.quantum.GlassViewEventHandler$MouseEventNotification.run(GlassViewEventHandler.java:323)
at com.sun.javafx.tk.quantum.GlassViewEventHandler$MouseEventNotification.run(GlassViewEventHandler.java:248)
at java.security.AccessController.doPrivileged(Native Method)
at com.sun.javafx.tk.quantum.GlassViewEventHandler.handleMouseEvent(GlassViewEventHandler.java:365)
at com.sun.glass.ui.View.handleMouseEvent(View.java:525)
at com.sun.glass.ui.View.notifyMouse(View.java:891)
at com.sun.glass.ui.win.WinApplication._runLoop(Native Method)
at com.sun.glass.ui.win.WinApplication.access$300(WinApplication.java:39)
at com.sun.glass.ui.win.WinApplication$4$1.run(WinApplication.java:112)
at java.lang.Thread.run(Thread.java:724)
Caused by: java.lang.reflect.InvocationTargetException
at sun.reflect.NativeConstructorAccessorImpl.newInstance0(Native Method)
at sun.reflect.NativeConstructorAccessorImpl.newInstance(NativeConstructorAccessorImpl.java:57)
at sun.reflect.DelegatingConstructorAccessorImpl.newInstance(DelegatingConstructorAccessorImpl.java:45)
at java.lang.reflect.Constructor.newInstance(Constructor.java:414)
at javaapplication36.ControlsSkinsApp$ControlsSkinsScene$1.handle(ControlsSkinsApp.java:81)
... 48 more
Caused by: java.lang.IllegalArgumentException: Children: duplicate children added: parent = DatePicker[id=SELECTED_NODE_ID, styleClass=combo-box-base date-picker]
at javafx.scene.Parent$2.onProposedChange(Parent.java:456)
at com.sun.javafx.collections.VetoableListDecorator.add(VetoableListDecorator.java:199)
at com.sun.javafx.scene.control.skin.DatePickerSkin.<init>(DatePickerSkin.java:69)
... 53 more