Firstly, it sounds as though your players are doing a lot of the heavy lifting for you in that they are being very easily manipulated without much effort on your part at all. But let's talk about manipulation.
Pa-pa-pa-poker face
Manipulation relies on getting people to do something without them knowing exactly why you want them to do it, or even that you want them to do it at all sometimes. Why? Because if they knew your reasons, they most likely wouldn't do it, and that doesn't help you. So lying. Your duke should agree to pay these adventurers anything they want if they do the tasks required of them. And he will lie. Oh will he lie. He will lie gleefully and to their faces, especially if they are silly enough to just blithely believe everything he says to them.
But what if they don't believe him...
Believable lying for beginners!
The best lies rely on two key concepts.
- A kernel of truth
- An appeal to emotion.
Let's go through them.
1) The more outlandish the lie, the less likely that someone will believe it. This seems like a common-sense thing, but people have a hard time with it. The best way to lie, then, is to distort or stretch the truth. Maybe the kobolds really do fear the dragon and want it dead because it could kill them all. It just also happens that a dead dragon means its horde is ripe for plundering, but the kobolds won't mention that they plan on taking all of that treasure for themselves. Why bring it up?
And an important thing to remember here: if you're playing someone who is actually manipulative, they will not seem stereotypically manipulative or as though they are lying. No long pauses or sideways glances, no hemming and hawing over details, no emphasizing exact wording ("I won't take your treasure." etc.) Lie. Lie right to their faces. Straight faced and unabashedly. It's amazing what people will buy if you just don't call attention to yourself and your weird behaviors.
2) Appeal to emotions. The players must care about some things. A manipulative person can tap into those desires. If your party is obviously in it for the wealth, maybe the duke talks about all the hidden treasure that would be "too much of a hassle" for the kobolds to dig out themselves, but the heroes are welcome to any of it they find along the way. If the heroes are sympathetic to the plight of the underprivileged, perhaps the thing the duke wants them to do is causing famine or disease, or is hurting the poorest of the community. "Really, it would be better for everyone if someone stopped it, but darn it I just don't have the resources to." Say anything to get them to agree. That's the point.
You lying bastard!
When the PCs do find out they've been had, there are one of two ways the duke can play it. He can try the "it was a misunderstanding" approach if he hopes to manipulate them again, but more than likely he will just be dismissive. He presumably has a contingency of kobold soldiers at his disposal, an army should be more than enough to take care of any PCs. Into the arena pits they go! (The duke may want to ask for more soldiers from his emperor while the PCs are away. He knows he lied to them and knows that they'll be pissed and knows they were capable of killing a dragon.) Don't make it a big show either. If the PCs call him out for his lying ways, he just accepts it. No reason to care what they think, they aren't kobolds and so they are inferior.
I don't think this is a good idea. D&D can scale down to one or one and half players (a "GMPC"), but the official pre-written adventures aren't meant for it. You'll spend more time mucking with the balance than is really worth it. And, I think there are plenty of reasons a GMPC is never a good idea — but even if you disagree on that, I think with only the two of you, the point stands.
I suggest either:
- Skip Lost Mine of Phandelver. Look on DM's Guild or another similar site for adventures intentionally written for one player. Citation: I tried to run this adventure with two players, and it didn't go well. But, there are good pre-written options out there — just not official ones from WotC.
- Find a few more people to invite to the game. D&D really works best with a party. I realize this gets heavily into personal advice, and there may be plenty of reasons this doesn't work for you — so, in that case back to option one.
Best Answer
You can have a NPC that is the BBEG.
There are a number of ways to have the ultimate enemy of your players accompany them at times during their adventures.
Multiple interactions is doable
The Curse of Strahd adventure opens with guidance about the players interacting with the boss multiple times (p. 10, under "When Strahd Attacks"):
A DMPC is a contradiction in terms.
A dungeon master is not a player by definition. A PC is a player character. Any other character is a non-player character. A DMPC is just an NPC that the DM has some special attachment with. If anything, that attachment may be a liability for the story and fun of others at the table because it could be put above them.