I interpreted the cards as her feeling wealthy and optimistic about this project. I saw the King of Diamonds as my father (financial support and security), which is watching the other way than the king of spades' in my cards. I saw the king of spades as my brother in law, who is in fact emotionally distant and has a military-like personality and is currently not speaking with my father. The outcome was relying on my brother in law.
You asked to see the financial fate of your sister. And you found out her fate is in the hands of the King of Spades. The numerical theme reflects the emotional or internal state of the questioner so it doesn't reveal the outcome but shows what leads to the outcome. What I mean is that the numerical theme shouldn't be used in a predictive way. It's really showing you the core message. The 9 theme shows that someone is TRYING to make a new start but cannot because of the unfinished business. In this case, she has a great outlook (10 of Diamonds) and some financial support (King of Diamonds) BUT there's a roadblock to her new financial start in the form of the King of Spades. I think your interpretation is rock solid.
Further explanation....when face cards show up in a 3-card reading, we can explore the dynamics between them. In this case, we have two face cards with their backs to each other. This means the people represented by these cards are not speaking to each other, as the student mentioned in his background info.
What do you see? Share your insights in the comments section!