SampleContainerViewController.m

- (void)removeViewController:(BOOL)animated
{
    CGRect destInitialFrame = self.destinationFrame;
    CGRect destFinalFrame = CGRectMake(CGRectGetMaxX(destInitialFrame),
                                       CGRectGetMinY(destInitialFrame),
                                       CGRectGetWidth(destInitialFrame),
                                       CGRectGetHeight(destInitialFrame));
    
    UIViewController *srcViewController = self.sourceViewController;
    UIViewController *destViewController = self.destinationViewController;
    
    // 1. beginAppearanceTransition:animated:
    [srcViewController beginAppearanceTransition:YES animated:animated];
    [destViewController beginAppearanceTransition:NO animated:animated];
    // 2. viewのアニメーション
    void (^before)() = ^{
        // any pre-animation process
    };
    void (^block)() = ^{
        // animation block
        destViewController.view.frame = destFinalFrame;
    };
    void (^finish)() = ^{
        // 3. removeFromSuperview
        [destViewController.view removeFromSuperview];
        // 4. endAppearanceTransition
        [destViewController endAppearanceTransition];
        [srcViewController endAppearanceTransition];
        // 5. willMoveToParentViewController:
        [destViewController willMoveToParentViewController:nil];
        // 6. removeFromParentViewController
        [destViewController removeFromParentViewController];
    };
    if (animated) {
        before();
        [[UIApplication sharedApplication] beginIgnoringInteractionEvents];
        [UIView animateWithDuration:self.animationDuration delay:0 options:UIViewAnimationOptionCurveEaseOut animations:block completion:^(BOOL finished) {
            [[UIApplication sharedApplication] endIgnoringInteractionEvents];
            finish();
        }];
    } else {
        before();
        block();
        finish();
    }
}