When you play in Google's sandbox, you have to play by their rules. One of the biggest complaints I get from clients is the suggestions at the end of the video are either not relevant or worse, they are competitive videos. Here's an easy way to prevent your embedded videos from showing suggested videos at the end.
It's probably easier to show you so you can follow along.
Here is the embedded code straight from YouTube for one of my clients videos:
Here is the edited code after edit. Note the highlighted yellow... after you embed the above code, copy the highlighted portion (it will look different obviously for your video). Then edit the code as follows:
By making the video loop, it will never show the suggested credits. If the browser allows it, the video will also autoplay.
HERE ARE THE TWO VIDS (the top one is the looping vid). You can drag to get to the end quicker to see if it loops or shows suggested videos. Note if you stop the video, you will still get the suggested videos. Note also that on the first code sequence we have ?rel=0. By adding this, YouTube will select videos from your own playlist (assuming you're video is in a playlist you created). This avoids showing competitive videos even if the visitor presses stop.