It's still weird to me that the king had to remove his whole daughter from the royal family and then he didn't even talk to her or try to spend time guiding her correctly...as a father. Whew!
Being a King is a huge responsibility. Especially if they actually do care about the welfare of their people.
While it's possible that he could have her along with him as he works, there would be matters that he would be attending to where he absolutely could not have her around. Such as matters that involve state secrets.
Thus, she'd spend most of her time with tutors and nannies.
And, unfortunately, it seems that there were people who were aiming for more power. They saw an opportunity in this by making this girl into a figurehead and began grooming her as such. So, the absolute best thing to do was to remove her entirely from the power structure, get her physically away from the people who were trying to corrupt her, and into the hands of a trustworthy family member who would raise her with love, and instill proper morals into her psyche.
It was a very smart move on the part of the king. Especially since it drew out the traitorous elements in his court. Once it was known that the Princess was going to be relocated, the traitors would scramble to try and get people into position to continue corrupting her.
Now, I know you may be asking, "Why didn't they notice though? How did they not see this as an attempt to smoke them out?"
Simple. The King engineered a situation where his daughter's selfish ways would give him just cause to temporarily disown her. With this, the traitors would have thought that maybe they just pushed a little too far too fast on the Princess. So the "proper" reaction in that case would be to try to continue to influence her perceptions, though in a more measured way.
And the moment they started to prepare? That was where the King sprung his trap and started to clean house.
Unfortunately, it's gonna be a few years - probably even a decade - until it's safe for the Princess to return to her proper place in the capitol. Because while the King can certainly have all the suspicious parties arrested and the evidence seized, even for him the wheels of justice turn very slowly. Great care must be taken when prosecuting the Nobility of one's country, even if you are the King. The case must be airtight, the evidence incontrovertible, and the judgement inescapable. Otherwise, failure means that the troublesome elements not only got away, but also know that you're on to them. Which means they'll continue to make trouble, just in a more subtle and clandestine manner.
And, additionally, they can use it as a means to gather more allies. "Look at what that man tried to do to me! It might be you, next!"
It's gonna be a while for the Princess, but this is the absolute best for her.