He could also distance himself from them. Naruto might choose to avoid his family, not wanting to be around them as a way to show his anger. He could move out or stop participating in family activities.
His family might have neglected him in some ways. Naruto grew up alone and feeling unwanted in the original story. If in the fanfiction, his family was around but still didn't give him the love and attention he needed, it would be a valid reason for his anger. He has always craved connection and acceptance, and if his family failed to provide that, he would be furious.
He might directly confront her. Naruto is not one to hold his tongue, so he could just barge into Tsunade's office and start yelling about why he's angry. For instance, he could say 'Tsunade - sama, your decision was wrong and it's going to hurt a lot of people!'
He might lash out with his magic. For example, he could send a spell flying at the source of his anger without really thinking. Sometimes, he just glares intensely, his green eyes filled with fury. And he may raise his voice, shouting at those who have angered him.
He might try to prove himself. Naruto has always been a determined character. So he would likely strive to show his family that they are wrong about him. He could do this by achieving great things in the ninja world, like mastering new jutsus or completing difficult missions.
In some fanfictions, Naruto might forgive his family after realizing the circumstances that led to their actions. For example, if his parents had to make a difficult choice for the greater good, Naruto, with his big - hearted nature, could come to understand and forgive. He might have a heart - to - heart conversation with a family member's spirit or through a time - travel plot where he gets to see the past more clearly.
Well, it could go in many directions. For example, his family might start to search for him, which could lead to a series of adventures where they encounter new characters and face various challenges. His wife, if he has one in the story, might become stronger and more independent in his absence, vowing to bring him back.
It might make him more distant from his friends at first. He could be so consumed by his anger towards his parents that he withdraws from his usual social circle. For example, he might avoid spending time with Sasuke or Sakura because he is too preoccupied with his feelings about his parents.
He might put on a fake smile and act normal. Naruto is good at being energetic on the outside, so his family may not suspect that he's in pain.
Well, in fanfictions, often the plot takes a different turn. Naruto might hide from his family because there could be some sort of misunderstanding. For example, there could be false rumors about him being involved in something bad. And he might think that his family would believe those rumors without giving him a chance to explain. So, to avoid the immediate confrontation and judgment, he chooses to hide.
Maybe he has some personal grudges or misunderstandings within the family in the fanfiction. It could be that something happened in the past that made him feel betrayed or unappreciated, so he refuses to offer help.