refresh/reload angularjs custom directive

Add a watcher in first directive in link function.

scope.$watch('thingToWatchForRefershing', function (newValue, oldValue) {
    if (!newValue || angular.equals(newValue, oldValue)) {
        return;
    }
    scope.$emit('somethingChangedInFirstDirective', dataToBePassed);
});

Now, in your second directive, have a render function which when called will refresh the models and views and also add a listener.

link: function () {
    scope.render = function () {
        // all logic goes here
    };
    scope.$on('somethingChangedInFirstDirective', function (ev, data) {
        // render everything again i.e. reload the directive
        scope.render();
    });
    // first time rendering
    scope.render();
}

Hope it helps :)

Update:

1. Pass an attribute to the first directive only. eg: <custom-carousel data-is-to-be-watched="isToBeWatched" /> and in your controller set: $scope.isToBeWatched = true. Also, for the second directive use: <custom-carousel data-is-tobe-reloaded="isToBeReloaded" /> and in the same controller initialize: $scope.isToBeReloaded = false;
2. If its an isolated directive, having its own scope, then: have this scope:{isToBeWatched: '=?', isToBeReloaded: '=?'}, link: function (...) {...}
3. Once the directive is loaded, check if (scope.isToBeWatched), is true, it means first directive is loaded/changed since we passed the attr only in first directive. Now, emit an event, which will be listened in the controller. In the listener do: $scope.isToBeReloaded = true; which in turn will set the variable isToBeReloaded in the second directive's scope, since we passed in 2nd directive.
4. Have a watcher for isToBeReloaded and reload the render fn as I mentioned earlier.

Rough code:

Controller:

$scope.isToBeWatched = true;
$scope.isToBeReloaded = false;

$scope.$on('somethingChangedInFirstDirective', function () {
    $scope.isToBeReloaded = true;
});

Directive:

scope: {
isToBeWatched: '=?',
isToBeReloaded: '=?'
},
 link: function (scope) {
 scope.render = function () {
    if (scope.isToBeWatched) {
        scope.$emit('somethingChangedInFirstDirective');
    }
 };
 scope.render();

scope.$watch('isToBeReloaded', function (newValue, oldValue) {
    if (!newValue || angular.equals(newValue, oldValue)) 
         return; 
    scope.render();
})

}