hi Danny,
The below will work perfectly fine
var btnShowCal = $('#Screen1_mobiledatepicker_5').find('.datepickeropenbutton');
btnShowCal[0].click();
Just note that the component name is page name _underscore_component name
In my case the screen name is Screen1 and component name is mobiledatepicker_5
You can use this individually for each of your datepicker components. It works fine in the Click event of the datepicker. You can experiment with the tap event as well, if you wish to