Goku entered the Rosat with Vegeta/Gohan with Trunks?

[GSM123]

What if training partners were exchanged? What would be a reasonable in universe explanation for this swap? Who would go first? How would this affect the story?

 

[SSJ3 Gothic]

Interesting prospect.

Vegeta: I think Vegeta ends up about the same. He spent most of his time in the RoSaT training by himself. I don't see much changing if he went in with Goku, especially for where his character was at that time, which was highly overconfident and more of an arrogant asshole than usual.

Goku: He probably ends up being stronger than in the original story, since Goku would have been able to spend more time training and increasing his own power instead of focusing on Gohan. I don't think his ceiling raises terribly higher, since MSSJ seemed to max out the SSJ form, but I do see a bump here.

Gohan and Trunks: This is more interesting to me, because there's a chance that these two can recreate their bond from the alternative universe. The dynamic would be flipped, with Trunks taking on the role of the mentor and Gohan as the student. Trunks would certainly be motivated to train Gohan to his upmost because what Gohan did for him in the alternate timeline. We know Trunks makes the mistake of favoring USSJ. Since he's not forced to keep to himself as with Vegeta, Trunks probably shares the form with Gohan and the two of them train using that, basically making them useless. However, so long as Trunks gets Gohan to SSJ, which I believe he could, there's always the chance of Gohan getting pissed and achieving SSJ2 in the Cell Games anyway, so long as he gets pissed enough due to some triggering event.

TL;DR: things might end up the same

 

[Captain Cadaver]

Vegeta would insist on going in first, meaning Goku does so too. Focusing on his own training, he not only masters SSJ, but becomes stronger than he would in canon (let's say as strong as his Boo Arc self). Vegeta initially trains on his own, though starts sparring with Goku after the latter's mastery of Super Saiyan leads to him far surpassing Vegeta. Vegeta masters the form by the end of their training, coming close to Goku's level. Because of Goku not being outside, Cell would've killed Piccolo and Tenshinhan. The rage of Piccolo's death would cause Gohan to achieve Super Saiyan, though Trunks would still be able to restrain him from charging at Cell.
Once Goku and Vegeta emerge from the Rosat, Goku would tell the other two what they achieved from training and tell Trunks to try and aspire towards the same whilst teaching Gohan. Goku and Vegeta then confront Cell and things go the same until Vegeta agrees to let Cell become perfect. Goku tells Vegeta he'd have liked to see Cell's full power, but the situation having escalated with two of his friends' deaths are enough he won't allow things to get worse. Goku uses Shunkan Ido to immediately get to Cell and finish him off with a Kamehameha, though Vegeta isn't concerned. Cell was meant as the build-up to them settling the score and all Cell's death has done for him is quicken this objective. Vegeta then challenges Goku to a battle to the death in which they give it their all. Despite his best efforts, Vegeta is one step behind Goku and is eventually defeated, with Goku telling Vegeta he ought to try training for more than just defeating him if he wants things to be different.

Meanwhile, in the Rosat, Trunks teaches Gohan based on what Goku taught them and the two grow as friends, though Trunks' lack of experience in training limits the gains they make at first. However, Gohan's desire to avenge Piccolo drives him to train intensely. They manage to master the form by the end of the training, though are weaker than they would be in the main timeline. Gohan still makes studying his main focus as Chichi demanded, though trains enough in his spare time as to not weaken, and Goku starts working. Before Trunks heads back to his timeline, Vegeta decides to spend time training with him when coming to the conclusion perhaps the friends and family Goku has are what allowed him to stay a step ahead as a motivator, ending up the same as in canon by the start of the Boo Arc. Goku also heads to New Namek and Dende brings everything back to normal.

The start of the Boo Arc, one major change is that Goten's strength surpassing Gohan as well as Goku being there would lead to Gohan training intensely with his father and brother. This advantage and the greater experience Goku's presence would've had for Goten lead to him defeating Trunks in the Kids' Division. His father's presence would've had Goten be far more independent, not going along with Trunks' plan and preventing the Mighty Mask events. When the events on Babidi's Spaceship occurs, things go the same until the battle with Dabura, in which Gohan would still be at a significant disadvantage despite his training. Dabura deals significant damage, though Goku gets in the way before things get too serious. He and Vegeta do rock-paper-scissors and the winner kills Dabura. Vegeta has progressed enough through his training and Goku has made such little gains from being forced to farm for many years that the gap isn't great enough for Vegeta to want to go Majin. Babidi is killed and peace comes with ease.

The events of Super play out the same for the most part. Gohan not going through the ritual makes him far weaker in the ToP and is eliminated not long after Kuririn and Tenshinhan. This doesn't change much in the long run as Goku and Vegeta would still power through the weaker opponents and Kefla would simply be defeated by someone like Jiren.