For each 3 posts, show a different post type

There are several ways to do this. Here’s an easy one. Let’s say you want to mix 9 ‘daily’ posts and 3 ‘quotes’. First you would have to get those posts:

$dailies = get_posts(array('posts_per_page' => 9, 'post_type' => 'daily'))
$quotes = get_posts(array('posts_per_page' => 3, 'post_type' => 'quote'))

Next you would loop through them like this:

for ($i = 0; $i <= 9; $i++) {
  // html to output $dailies[$i]
  $j = (($i-2)/3) // will be integer if $i=2, 5, 7, so after three dailies
  if (is_int($j) {
    // html to output $quotes[$j]
    }
  }

You will need to add some extra logic to prevent errors in case there are less than 9 or 3 posts respectively.