I do not think there's an option for handling a double-click event for a date in RadCalendar. It is possible to open a RadAlert Window by handling the "OnDateClick" Client Event as follows:
function ShowRadAlert(sender, eventArgs) {
var day = eventArgs.get_renderDay();
var date = day.get_date();
var selectedDate = new Date(date[0], date[1] - 1, date[2]);
radalert("You clicked " + selectedDate.toDateString(), "200px", "100px", "Calendar Date Clicked", "");
}
The only alternative is to use the RadScheduler Control which does provide the "OnClientAppointmentDoubleClick" event. You can view this in the Scheduler / Client-side Events online demo.