It is never a good idea to have a 'best friend' relationship with a member of the opposite sex who is not already your spouse. My husband is my best friend, and I, his. Keeps things simple. Works well if you can wrap your head around the concept of safe love. Most people can't.
This is my opinion and advice...tell her to choose between you and the best friend. She cannot have two men in love with her at the same time, no matter what her intentions! It will end badly, one way or another. By turning to your wife for comfort his wife will not give, he is alienating her affection for you.You could sue him It's best to end it now, while the pain is still small. Tell him to get a counsellor, he can't have your wife.
Don't act too heavy handed with your wife, or she might rebel. Speak to her gently, lovingly, but firmly. Tell her you are not okay with the friendship, that its not about trust, its about propriety...what's right and wrong. It is right that you be her best friend forever, not another man outside the marriage, Real love, marital love demands both partners forsake everything and every one outside the relationsip, even completely platonic best friends forever.
Furthermore, if this situation is bothering you it's a threat to the marriage, plain and simple. You need to decide if you're willing to risk losing her by giving her an ultimatum, because she may choose him. However, in my opinion, if she does that, your marriage was already broken.
She needs to realize you are the appropriate BFF. Not him, not anyone else. Furthermore, this guy shouldn't be leaning on the shoulder of another man's wife, He should be seeking counselling and consolation from another man who can relate to his marital difficulties and offer what he needs, understanding and sound advice, not a soft sholder and a sympathetic ear.