Hi Michael,
Right now there is no events in DatePicker for Done and Cancel actions. But the events available in DateSelector control. So we create a sample in which we handling the events of DateSelector that is present inside DatePicker control. We have attached the sample for your reference.
Please check the sample and let us know whether it meet the requirement.
[Sample link]: http://www.syncfusion.com/downloads/Support/DirectTrac/General/DateTimePicker_Demo1011755602.zip
Please let us know if you have any concerns.
Regards,
Karthikeyan L.