I was surprised at how much I was enjoying your story. The girl is mostly believable, her reluctance to have their relationship discovered is quite rational. His parents have the power to destroy her if they choose. Certainly royals have their little scandals, but sometimes a mistress can become an issue outside the bedroom.
If they see her as a problematic influence on him... an accident could be arranged so they do not have to face their son's wrath for acting openly and directly.
I am glad you were sketchy on the economics of the kingdom and taxes, most people don't know enough about the subjects to be credible.
If you are interested, I can recommend a few books and writers. One I remember involved priorities for improving 3rd world countries. Development as Freedom is a surpisingly good read.
So many sources I could refer you to... I urge you to avoid utopianism when the Prince starts trying to fix things in the kingdom. Human Action by Von Mises is revealing, and there are online courses discussing it.
The history of socialism tracks through a lot of death and destruction. In spite of all the gruesome failures, there are people who think that it will work this time if only they or those they support are doing it this time.
They don't even understand fully why it keeps failing- they don't want to understand. It is like a religion, faith based. Evidence and experience don't matter. Analysis and understanding doesn't matter. They want to create heaven on earth so anyone against them is against Heaven itself - and therefore evil.