Max McKeown's Answer:
A bad beginning makes a bad ending. It's easier to find a solution if you describe your problem in way that makes it possible to find a solution. If the problem is impossible, in your opinion, to solve, or the way you look at the problem makes solutions impossible to solve, then finding a solution makes much more difficult. Worse Ė putting a solution into practice becomes unlikely.
First, decide, is the situation with your Number two impossible? You can't sack him, you need him, he won't work with you, he is damaging your credibility, damned if you do, damned if you don't, between the devil and the deep blue sea, a workplace catch-22, poor, poor you, time to pack up your bags, and break down in tears on a sympathetic shoulder, or grab a bottle, syringe, or tub of Ben-and-Jerry's Phish Food ice-cream.
Maybe, it's just "nearly impossible" which isn't the same thing at all. See there's a big difference between nearly impossible and impossible. With nearly impossible: it's slightly possible With nearly impossible, there's hope, there are options. You never know, you might find a solution.
Second, accept responsibility. A bad workman blames his tools. A bad leader blames her fools. Being a manager involves managing people, coping with people, inspiring people. That is the job. And not just when they are your hand-picked buddies, perfect at their jobs, happy, smiling, and devoted to you.
Good managers need to start with the person, the situation, and the options available. All I know about you is that you managed to be in the right place at the right time to get the job ahead of the guy who thinks he was the right guy for the right job.
If you decide to stick it out, then either you win and he stays, or you win and he moves on (promotion or transfer Ė doesn't really matter which). He doesn't have to stay happy, he just has to stay doing a good job that makes you happy. And at some point he has to understand that. You might as well also find out what your formal options are if you conclude that his behavior is unprofessional. But you had better be professional first.
Give him the responsibility he craves. Test him out. Give clear tasks. Clear areas. Clear ways of assessing him. And keep him focused on what he is responsible for doing. Sometimes that means no arguments. Not taking BS. If he acts like a naughty child then stick him in the corner.
But don't assume he will act up. He's a grown man. Maybe he going to shape up quickly once you do your job in a way that he can respect.
Third, figure out the man. What makes him tick? What does he love? What makes him laugh? What's he afraid of? How does he spend his time? What gets him annoyed? What gets his competitive juices flowing?
Challenge him to something. Thumb wrestling? Learn to speak his language. Football? Baseball? Flower arranging? Community? Church? There's always something. Have fun. You're not begging him to be your friend but understanding how to interact in a way that you both enjoy is part of leadership.
Build up a flow chart of where you are and what you can do. And then enjoy being ahead of him, giving him, and the team, direction and purpose. Get him those qualifications he has been putting off for years. Knowing where you are going and how you're going to get there.
I make no apologies for not giving you neat answers with a script of what to say and when. Getting the job was the easy bit. Be a leader. That's what they pay you the big bucks for.