What happened is kinda simple:
Rina asked for funds for the orphanage, most likely on monthly basis.
King ordered the royal treasury to allocate the money.
Royal treasurer, or his aide, send the money to the local lord, who is supposed to be the sponsor of the orphanage, with the decree what these money are to be used for.
The local lord ignored the decree and kept the money for himself.
Royal treasurer, or his aide, send the money to the local lord, who is supposed to be the sponsor of the orphanage, with the decree what these money are to be used for.
This. This is the part that makes no sense. You're delivering a reward to someone to deliver a reward to someone, it's an unnecessary 3rd party. If Rina is too young to take it directly, you give it to her guardian. Her guardian is the orphanage director, the one who oversees the orphanage. The money should go directly to him, not the local lord.
Next is Rina even asking for funds for the orphanage in the first place. The local lord is supposed to be the sponsor of the orphanage which means he is suppose to be giving funds to the orphanage so why would Rina ask for monthly support? This thought never crossed the king's mind.
Missing the point here. The king cannot micromanage everything. He may have sent a messenger as you said but unless that messenger is someone of a standing that can be compared to a royal, the lord of the land can intercept it and the messenger cannot do anything about it and the king would only get a notice that the money was given to the lord of the land and king wouldn't bat an eye about it because as I said, he cannot micromanage everything.
I agree with micromanaging but you don't send a messenger to deliver funding especially from the royal treasury even more so if it's the reward for saving one's country. Since this is a matter of honor, someone with authority such as a royal knight or guard (most likely one with noble background) would either be the one delivering or accompanying the one delivering. A lord of the land can certainly intercept it but they will be met with someone of higher authority. Remember, a guardsman or knight working under the decree of the king has the power to admonish, arrest or even slay a noble. A noble trying to intercept funding from the king meant for someone else will be met with resistance....unless it's a newbie who knows no better.
And besides, the kid told the king to give her rewards to the orphanage so he in turn, just gives the money to the lord that where the orphanage is just like how our IRL Government Financing works.
IRL Government Financing most certainly don't work like this. I'm not sure where you're from so I have to base this off where I'm from but:
King = President
Local Lord = State Mayor
Rina = Citizen who's a minor
Orphanage Director = Rina's legal guardian.
With this in mind, lets say Rina solved some problem that saved the country from a fallout. She meets with the president and is promised a reward. They can't give the reward for her directly so they arrange for her to receive it monthly. What the government will NOT do is send it to her State Mayor and entrust him give it to her. They are going to have it sent to her legal guardian.
Basically, this is nonsensical plot point that really shouldn't have happened in the first place.