Prince Guide
Princes are incredibly tragic figures. Halfway between a thief and a lord, but not quite able to pull off either. They have the jerk insticts of thieves, but aren't comfortable with expressing it. They have the same controlling urge as lords, and hate themselves for it. This is the core of what being a prince is. You have all these insticts and drives that are in constant conflict. You do stupid things, and don't understand why. You wish you were anyone else.
One of they key traits of a prince is the cycle of self destruction. Princes hate themselves. Much more than thieves or rogues, and in ways that they don't understand. They will actively do things against their best interests. Act like jerks when they don't want too. Be overly abrasive, be overly clingy, and hurt everyone around them. And when this happens, they all do the same thing. They run away. Physically, emotionally, whatever.
Bojack Horseman went to Arizona. Jesse Pinkman turned his home into a crackhouse. Rick Sanchez fucked off into space and it's countless alternate dimensions. Dr. Manhattan built a castle on Mars. Chuck Mcgill baracaded himself in his home. Always the same pattern. Always trying to escape themselves.
Princes have all the same insticts as thieves. The ego, the drive, the aggresiveness. But they also need to be liked by people. They want to love, and be loved in return. This conflict is what drives princes through life. Displays of good will and affection, followed by spirals of self destruction. It's a constant battle for them, the need to balance these forces.
They can look like Lords from a distance. Once they bond with someone, they can be very controlling. The difference is that princes feel bad when they fuck up. Lords are always looking out for number one, they don't care who they hurt in this process. But princes do. They care so much, even though they might not show it. Hurting someone triggers waves of self-hatred, leading to fatalistic spiraling. Isolation, running away, they always fall back into the same cycle.
Bojack Horseman is the de facto example. It's all there with him. The self destruction, the need for others love and aproval, the fluctuating ego, and just having a hole that will never be filled. Anyone with that upbringing, combined with that kind of star status isn't going to turn out well. He's broken at this fundamental level. He can do good things for people, and he can be "nice" but not consistantly. He's always one bad day, one mistake away from self destructing and reseting back to stage one.
Prospit Princes
The controlling, possessive, and clingy aspects of a prince are more prevelent here. They have a very specific way of how you should live your life, and they'll impliment it by force if they need too.
Derse Princes
Derse princes are the ones to worry about. A lot of the "tortured genius too smart to be happy" trope is here. They may initially appear to be laid back, confident, and self assured, but like so many dersites, these are just masks they use to hide someone who doesn't know who they want to be. At their core, princes are weighed down by intense self hatred and self destructive tendances.
Eridan is the first example we get from Homestuck, but doesn't hold up well under close inspection. He leans more towards Lord, and Hussie even admits Caliborn was designed as a more thourough exploration of his archetype. Dirk works a lot better, certainly with his 10,000 IQ mindgames and confusing mixed signals. The way he flirts with Jake is very similar to how thieves flirt, just jacked up to 11, with an additional 20 layers of self-aware (possibly self hatred) irony.
Closing Thoughts
It's hard being a prince. It's hard and nobody understands.
I don't have much to give in terms of technical advice. Rogues are the neighbors of princes, and I fall into my own mini version of that cycle, where you push everyone away and self destruct. I don't know a cure for it.
And I think when we can't change something, it's best to try and accept it. If anything, little changes are a place to start. Just try your best to do right by others around you, and I think we'll all be ok.