I think its more like to not just dumping and seeking help to your commander in every problem that can be solve by yourself. She did not told it to the commander because she knows that she can handle it herself. Asking for help to your commander despite knowing that u can solve it urself is kinda not good for a self feeling, FOR ME it's like you'll feel useless because u did not solve the problem despite knowing how to solve it. In MY OPINION judith can solve it by winning in a duel with that thing in their feet. And for the prince joke it's like you got appointed as a commander because of your hardwork and liking the job or position that u are now in but suddenly saying you can't handle it anymore can lose your pride as a person who is holding that position liked by many people.
I don't think he was joking. He was trying to tell the commander to put himself in FL's place and think about the situation from a different perspective.
Since the commander has shown faith in FL's ability and has also extended the position of Vice-captain to her, it will naturally be harder for her to go to the commander for help. Like how the commander will not go to the king, who appointed him as the commander, for help because he probably doesn't want to appear incompetent in front of his superior. (king)
Another thing also is that the commander is saying that he is upset because the FL didn't come to him for help even after he told her to, because our boy is catching feeling for FL without even realizing it and the 4th prince was sympathizing with him because the feeling of not being approached for help from the girl he likes is also adding to his awkwardness.
Phew! that was a long ass explanation! ( ̄∇ ̄")

Can someone explain the joke the prince made? About telling the king that he cant handle being a commander anymore?