Goals, Motives, and Purposes, Part IV
What your characters want
This builds on Part I, with the fourth example — slightly expanded to give some setting.
Joan is the daughter of a prince and a merchant's daughter, who were married off by a tyrannical king against their will, because their children could not inherit. As soon as the king died, the couple swore in a church court that they had married against their wills and were separated. They both remarried, but raising her at court might raise her hopes falsely, and raising her among merchants would let intriguers use her. She was packed off to a cousin of the king's as his foster daughter. She wishes she could drink of the cup of sovereignty as acknowledgment that she was the prince's daughter, but knows she could cause war and disaster in the realm, and would thus be unfit to be a sovereign.
This is a motive that will not drive her actions -- directly. It is a form of characterization.
More or less indirectly is possible. If her kingdom is invaded, and all heirs recognized by the law die, the subjects may turn to her in preference to the conqueror. Or marry her off to the next heir because he's distant. (Laws of inheritance tend to get flexible when they can't produce an heir.)
Even in such a story, the bitter knowledge that she's her father's heir because no one has any choice in the matter, and that her father had never, and would never have, acknowledged her as such, lends an edge to her actions.
Likewise in a romance, where she knows for a fact that her father will insist on his consent to a match. She has the bitter knowledge that her father will give a jaundiced eye to any man proposed as her husband, and that even any implausible problem will be reason to block it. On the other hand, if she married without his consent, then she and he might have to flee the kingdom and would have a hard time finding refuge. Only her kingdom's enemies would be willing, and that would be irresponsible on her part.
If she lives more mundanely, mastering the arts of managing a household, becoming a wizard, or going on a pilgrimage in the course of a story, the bitter awareness of how her life is impossible cramped with both being and not being a royal daughter, and without even the freedom that being illegitimate would win her.
This can all be very fun, but it's all secondary. This can be the deep current under her motives, purposes, and goals, but it can not be the chief motive of her story, because -- as I have described it -- it is a negative motivation, a motive to not do something.
If this is the undercurrent, there has to be a current. She enrolls in a wizard's school because it's a suitable profession, and wrestles with her studies.
If she has to wrestle with the sneers of those who think that all royalty are spoiled, and with the flattery of those who think she can get them favors from her father and so, to make it easy for her, refuse to actually teach her the hard stuff, she will have motives, purposes, and goals. Enough to keep her going, keep the story going, and give the sharp desires for the impossibility something to act on.
She may even console herself with the knowledge that everyone would flatter her work if she were an acknowledged princess, and so she would know no progress. She's better off without it.
The deep question is whether she finds, in her story, enough community, esteem, and purpose, to assuage the wound left by her parents' rejection. This must be implied as strongly as the original wound to resolve the story.