AngularJs view not updating when parent property is changed from child controller - angularjs

Question

I'm trying to play around with extending controllers so the same code can be used in multiple places but extended with additional functionality where required. eg. when some functionality is available to some users but not others.
So I'm starting with a little experimentation with a very basic example. I have a simple controller and a more advanced controller that I extend with the simple controller. It all works so far, except when a function in the simple controller changes a property, the view doesn't update, although the property does update.
var app = angular.module("myApp", []);
app.controller("myCtrl", ['$scope', '$http', '$anchorScroll',
function($scope, $http, $anchorScroll) {
var vm=this;
vm.base_property='this is the base';
vm.baseFunction = function()
{
console.log('base function pressed');
vm.base_property='base function pressed';
console.log(vm.base_property);
}
}]);
app.controller("myCtrl2", ['$scope', '$http', '$anchorScroll', '$controller',
function($scope, $http, $anchorScroll, $controller) {
var vm=this;
angular.extend(vm, $controller("myCtrl", {
$scope: $scope
}));
vm.extended_property='this is extended';
vm.extendedFunction =function()
{
vm.extended_property = 'extended pressed';
}
}]);
<div id="app" ng-app="myApp" ng-controller="myCtrl2 as cal">
base Property: {{cal.base_property}}<br />
<button ng-click="cal.baseFunction()" >Base Function</button><br />
extended Property: {{cal.extended_property}}<br />
<button ng-click="cal.extendedFunction()" >Extended Function</button>
</div>
So clicking the extended function button , the text in the view for cal.extended_property updates, but clicking the base function button, the console output indicates the function is run and that the base_property has been updated but the value in the view doesn't change
I tried added $scope.$apply() but that just throws an error Error: [$rootScope:inprog] http://errors.angularjs.org/1.6.4/$rootScope/inprog?p0=%24apply (not ideal anyway as the real script is a lot more complex and I didn't want to have to be running that every time the base controller changes a property)
If there's a better way to achieve what I'm trying to do that isn't too complicated, I'm open to that too. Essentially I have a controller and I want to, in some circumstances, add additional properties and methods to that controller and ideally have it function seemlessly as if it were all the 1 controller