Looks like a good use case for $broadcast
:
$rootScope.modalAlert = function (alert_type, message, acknowledge) {
$rootScope.$broadcast('modal:start-open');
return $modal.open({
...
And then in your controller:
var AlertModalInstanceCtrl = function ($scope, $modalInstance, data) {
$scope.$on('modal:start-open', function() {
$modalInstance.dismiss('cancelled');
});
...