Instead of using $parent and an isolate scope, use $parse.

Instead of using $parent and an isolate scope, $parse can be used to specify which scope function the directive should call when a date is selected via the jQuery plugin UI.

There have been some discussions on StackOverflow about using ngModel
and isolate scopes.  The general concensus seems to be "don't":

http://stackoverflow.com/questions/11896732/ngmodel-and-component-with-isolated-scope

http://stackoverflow.com/questions/15419629/angularjs-two-way-data-binding-fails-if-element-has-ngmodel-and-a-custom-direct/15419873#15419873
"Since you are trying to create a component that must interact with other
directives, an isolate scope is not the best choice."