Problem with locking up the castle

There are several problems I saw with the story, but one of the dumbest ones was closing up the castle so nobody but two servants could be in there with the royal family.

This makes absolutely no sense, because in a small kingdom like that, unless the king and queen had an alternate government building to do business in, like a city hall, that castle serves as seat of the Arendellian government. You do not close up the entire castle just because you have a problem with ONE CHILD, supernatural or not. Shutting up a home like that may work for a middle-class family in a suburban neighborhood in America, or maybe a secluded home for a rich family, but it just doesn't work for the most important family in a small kingdom.

I mean, how are you supposed to have council meetings? How are you going to communicate with local officials to find out how the kingdom is doing? How are you to meet with foreign dignitaries? How are you going to conduct trade or other business? What if you have VIP guests? Kingdoms like Arendelle are far too small to be really self-sufficient. Often they only can survive through trade, because usually there's something missing from the area that a nearby country might provide. Living in a fjord is particularly difficult, no matter what era you live in. Not much fertile land, rocky terrain, weather is twice as harsh as normal in the winter, possible storms in summer, and mining anything would be difficult in steep mountain country like that.

The king and queen could have easily given Elsa her own wing of the castle to stay in, with a single trusted servant to see to her needs, and keep it secluded from all other parts of the castle so that business can carry on normally. They also had no reason the close up Anna along with them. Anna could have carried on a normal princess's life and been able to go out.

The only reason they set up this part of the story was so Elsa would feel isolated, and so Anna would end up a very sheltered, ignorant girl. The trouble is, it's a very weak part of the story that doesn't make sense, even from a fairy-tale standpoint.

I think the writers didn't want the setup I would have suggested, because then it would have caused a severe divide between Anna and Elsa. Anna would have had a life outside of the castle, and if Elsa could see her sister in action all the time from a window, she would have gotten jealous, and the relationship between them would have had a nasty wedge driven into it, causing them to become enemies. Anna might also have not fallen for Hans' fake charms as easily as the shut-in Anna did.

Again, the shutting up of the castle makes no sense, so they left it in for the sole reason of helping the story along.