^^Well said, Tolt.
You need to figure out what he is lacking in his training. Mules do not have the same mentality as horses and cannot be trained the same way that horses are. I've been around mules my entire life ranging from miniature to draft size and we have never needed anything more than a simple snaffle on them because they got all the right stuff put into their training.
If you don't have a lot of experience with handling mules, then I suggest you seek hands-on help from someone who does. Mules are very smart creatures and that can often be construed as stubborn or pig-headed. That is often not the case, they just need a good reason to do what you are asking and "Because I said so" is not a reason that they accept.
Unlike a horse, you cannot force a mule to do something he doesn't want to do and if you try, he'll turn sour very quickly. They don't forget anything and if you ruin his trust and respect for you, you'll probably never get it back.