After brainstorming, I've devised a solution for my project. Now, let's delve into the routing section.

var cartangularPublicShoppingApp = angular.module('cartangularPublicShoppingApp', [
  'ngRoute',
  'CategoriesController',
  'CategoryServices',
  'CategoryNavigationServices',
  'MenuModule'
]);
cartangularPublicShoppingApp.config(['$routeProvider',
    function($routeProvider) {
        $routeProvider.
            when('/categories/:categoryId', {
                templateUrl: 'partials/public/categories.html',
                controller: 'CategoriesController'
            })
    }]
);

---

This serves as the main controller for the view (categories.html), showcasing our custom directive. To test this directive, I've set up a mock dataset named "treeFamily" within this controller.

var categoriesControllers = angular.module('CategoriesController', []);

categoriesControllers.controller('CategoriesController', ['$scope', '$routeParams' , '$location', 'CategoryService',
  function($scope, $routeParams, $location, CategoryService) {

      $scope.treeFamily = {
          name : "Clothes",
          categoryId : "4",
          children: [{
              name : "Clothes",
              categoryId : "3",
              children: [{
                  name : "Men's Clothes",
                  categoryId : "2",
                  children: []
              },{
                  name : "Jackets",
                  categoryId : "1",
                  children: [
                      {
                          name : "Light Jackets",
                          categoryId : "4",
                          children: [{
                              name : "Natural Material",
                              children: []
                          }
                          ]
                      },{
                          name : "Heavy Jackets",
                          categoryId : "3",
                          children: []
                      }]
              }, {
                  name: "Pants",
                  categoryId : "4",
                  children: []
              }]
          }]
      }

---

Below is the directive we'll utilize for recursively traversing our dataset.

angular.module('MenuModule', [])
.directive("tree", function(RecursionHelper) {
    return {
        restrict: "E",
        scope: {
            family: '=',
            'product': '&products'
       },

        templateUrl: './partials/public/family.html',
        compile: function(element) {
            return RecursionHelper.compile(element);
        }
    };
})

---

I stumbled upon this compiling service online which ensures clean and organized code structure.

var categoryNavigationServices = angular.module('CategoryNavigationServices', []);
categoryNavigationServices.factory('RecursionHelper', ['$compile', function($compile){
    var RecursionHelper = {
        compile: function(element){
            var contents = element.contents().remove();
            var compiledContents;
            return function(scope, element){
                if(!compiledContents){
                    compiledContents = $compile(contents);
                }
                compiledContents(scope, function(clone){
                    element.append(clone);
                });
            };
        }
    };

    return RecursionHelper;
}]);

---

Here's a snippet of html fragment depicting our directive in action, calling itself from within the directive.

<a href="javascript:void(0);" name="categoryId" ng-click="product(family.categoryId)">{{ family.name }}</a>
<ul>
    <li ng-repeat="child in family.children">
        <tree family="child"  products="products(child.categoryId)"></tree>
    </li>
</ul>

---

Additionally, here's a segment from my categories.html page – the primary view from my controller.

    <ul>
            <li ng-repeat="object in treeFamily.children">
                <a href="javascript:void(0);" name="categoryId" ng-click="products(object.categoryId)">{{object.name}}</a>
                <ul>
                    <li ng-repeat="child in object.children">
                        <tree family="child" products="products(child.categoryId)"></tree>

                    </li>
                </ul>
            </li>
   </ul>

---

While addressing issues with the recursive directives, one problem stood out - the ng-click added to the directive's html wasn't responsive due to an isolated scope.

To resolve this, binding the directive's method to the controller's method was necessary. This meant adding the controller's function to be bound within the directive tag itself:

<tree family="child" products="products(child.categoryId)">

The directive's isolated scope references this setup:

scope: {
            family: '=',
            'product': '&products'
       },

Inside the directive's html, the a href link looks like:

<a href="javascript:void(0);" name="categoryId" ng-click="product(family.categoryId)">{{ family.name }}</a>

Notably, the directive's function "product" is referenced instead of "products," which denotes the desired controller method access.