performSegueWithIdentifier doesn't work

You need to wait until your other view controller is done animating, before performing the segue. You can use the new iOS 5 method:

[self dismissViewControllerAnimated:YES completion:^() {
    [self performSegueWithIdentifier:@"My Segue" sender:self];
}];

If you need a pre-iOS 5 way to do it, you should just add a delay to give the animation time before performing the segue.