Add child view controller to UINavigationController

@Sam's comment is correct. You need to call beginApperanceTransition:animated: and endAppearanceTransition for viewDidAppear to be triggered. The reason why UINavigationController does not call viewDidAppear when you add a child view controller is because it has overridden its container composition methods to prevent the programmer from adding a child view controller in strange places. In your case, it doesn't want your child view to cover up the navigation bar. The correct usage of a navigation controller is to have children appear under the navigation bar. Nonetheless, you can still force upon this non-standard UI by manually telling the child when it is appearing and when it has finished appearing.

Add a child to UINavigationController

MyChildViewController* child = [[MyChildViewController alloc] init];
[self.navigationController addChildViewController:child];
child.view.frame = self.navigationController.view.bounds;
[self.navigationController.view addSubview:child.view];
child.view.alpha = 0.0;
[child beginAppearanceTransition:YES animated:YES];
[UIView
    animateWithDuration:0.3
    delay:0.0
    options:UIViewAnimationOptionCurveEaseOut
    animations:^(void){
        child.view.alpha = 1.0;
    }
    completion:^(BOOL finished) {
        [child endAppearanceTransition];
        [child didMoveToParentViewController:self.navigationController];
    }
];

Remove a child from UINavigationController

[child willMoveToParentViewController:nil];
[child beginAppearanceTransition:NO animated:YES];
[UIView
    animateWithDuration:0.3
    delay:0.0
     options:UIViewAnimationOptionCurveEaseOut
    animations:^(void){
        child.view.alpha = 0.0;
    }
    completion:^(BOOL finished) {
        [child endAppearanceTransition];
        [child.view removeFromSuperview];
        [child removeFromParentViewController];
    }
];

In your first view controller, do something like this:

- (IBAction)buttonClick:(id)sender
{
    SecondViewController *secondView = [self.storyboard instantiateViewControllerWithIdentifier:@"SecondViewController"];
    UIImage *blurryImage = [UIImage imageNamed:@"foo.jpeg"];
    secondView.imageView.image = blurryImage;
    [self.navigationController addChildViewController:secondView];
    secondView.view.frame = self.navigationController.view.frame;
    [self.navigationController.view addSubview:secondView.view];
}

Then in your second view controller, add the getter for your imageview:

-(UIImageView *)imageView
{
    if( _imageView == nil )
    {
        _imageView = [[UIImageView alloc] initWithFrame:CGRectMake(0, 0, 320, 548)];
        [self.view addSubview:_imageView];
    }
    return _imageView;
}