Once The Dragon Team flew over to The Son House. They told Chichi the news about Goku's sacrifice. Which caused her to break down into tears. After, Krillin comforted her by saying that Goku can be revived from the dragon balls. Roshi has mentioned Goten's request to her. The woman was curious while her son silently looked down. Then he finally dared to ask about the training. Chichi is vivid as she tells Goten that he cannot go and needs to study. The young Saiyan hybrid had enough of this and screamed at his mother. This made Chichi absolutely shocked and even unintentionally slapped Goten. Which caused him to run into his room and cry. The lady felt deep regret as she remembered the premature baby. Bulma came up to Chichi and said that they would talk to her son.
The group went to have a chat with Goten as they saw him crying in his bed. Bulma sat down next to him and wondered if he was okay. Feeling frustrated, the boy yells out, saying his mom won't let him be what he wants. The friends looked at each other as Bulma tried to be reasonable with Goten by telling him that Chichi was only giving him a good education. However, Goten is not buying it and wants to fight against the Saiyans. After some thinking, Roshi came up with a plan. He informed Goten that he would be doing turtle hermit training for six months and then Kami's for another. This made Goten very excited and thanks to the old timer. However, Roshi reminded him that he should wait until nighttime. So he can sneak up to Kame House while riding on the Nimbus cloud. Goten agrees and continues with his day.
As Goten arrives at Kame House, he unintentionally disturbs the old man's slumber. He profusely apologizes to Roshi and the turtle hermit just remembered his promise. So, Goten and Roshi traveled to a bigger island, where they transferred the house by capsule. Similar to Goku and Krillin's training, Roshi tested Goten by throwing a kanji-written rock into the jungle. The boy was confused and thought that he would learn martial arts. The old timer lost patience and told Goten to go get it. Anyhow, the next morning, Roshi gave the boy an assignment to deliver milk. The young Saiyan hybrid asked about martial arts again. So, the old man told him that he needed to do exercising first. Goten's tears came out of his eyes and threw a tantrum. This made Roshi snap as he informed him that he chose to do this training. The boy calms down and apologizes.
As six months go by, Goten learns the same kind of training that his father and Krillin went through, including wearing a heavy turtle shell. Once the training is finished, the boy feels amazed at how light he feels and thanks Roshi. Then the old timer gave Goten a Turtle Hermit Gi, a replica of Kid Goku's. Roshi felt proud of how mature this little boy was becoming. Before Goten leaves, Roshi reminds him that he will have to climb Korin's Tower and then the power pole before arriving at Kami's Lookout. The boy thanks the old man and flies off with his nimbus. Once he arrives, Bora and Upa recognize Goten's outfit and he looks similar to their old friend. The young Saiyan was confused by all of this, as he never met the two. Therefore, Upa told him the story of how Goku climbed the tower, defeated The Red Ribbon Army, and revived Bora by using dragon balls. Goten was amazed by all of this, as it made him respect his dad even more.
After many trials and errors, Goten finally arrives at the lookout. The Dragon Team was pleased to see him. They were amazed at how strong and mature he had gotten. Over the next six months, Goten learned martial arts techniques from Kami and Mr. Popo. Along with the other Z fighters, helping him gain his skill. Therefore, Goten has developed a bond with the group. Unfortunately for this scenario, Piccolo hasn't gotten a change of heart because he never trained the boy. His power level is also 1.61x lower compared to his canon counterpart. Although, this is nothing compared to Goten's. Whereas his power level is 1.82x lower than Gohan's due to Piccolo not training him. He's even weaker than Chaotzu.
Now, here is something that I have been wondering for a while and I want you guys to answer it. Do you want Goten's hair to grow or continue to have Goku's style?