Realising how outmatched he really was, Gohan knows not to head into battle again until he's fully prepared and decides letting Bulma complete the time machine is a better option. He continues to train Trunks and the latter becomes significantly stronger than in canon, being more or less post-Yardrat Goku's equal with Gohan being slightly above that. Both go in the time machine and, under Gohan's instruction, Trunks doesn't go kill Freeza and lets Goku handle it. They then inform him of the situation and Goku recommends they stay with him to train a while so that the present Gohan can unlock SSJ too. After a few months, they return to the future. Due to Gohan having become a Super Saiyan, he's considered essential enough that Piccolo tells Kuririn to go take Bulma and Yajirobe to Capsule Corp. With 3 Super Saiyans fighting #17 and #18, the twins have a difficult time, but manage to pick each one off one by one, other than present Gohan who they leave conscious to give out the Senzu. When it comes time to going into the Rosat, the pairings are the same, though Future Gohan plans to go in with his father and then Trunks once they've had their turns. Due to not being kissed by #18, Kuririn doesn't hesitate to shut her down and Cell is prevented from achieving his perfect form, being killed by Trunks therafter. After everyone has trained, Trunks and Gohan return to the future and kill both #17/#18 and Cell.
7 years later, Goku and Vegeta would've achieved SS2 and, whilst not as much as in canon, Vegeta would've somewhat warmed up to his family. Not training in Other World would mean the gap between Goku and Vegeta would be slim to none, meaning Vegeta would have no intention on being controlled by Babidi. Those two kill Dabura and the battle with Boo is averted.
As for Super, the events of Battle of Gods play out in a similar manner with Beerus simply getting bored and demanding the Super Saiyan God rather than being pissed off at his pudding getting eaten, with FnF being entirely the same. The Universe 6 tournament sees Boo being replaced with Gohan after Goku pleads with his son to join. Even assuming he hasn't slacked off though, he gets beaten fairly quickly if participating at all. With the Future Trunks Arc, Gohan and Trunks training together on the Kaioshinkai would make it unlikely they wouldn't stop Dabura before Shin died (perhaps even achieving SS2 prior to the battle), so the entire Goku Black situation is averted for this timeline. He and Zamasu go to some other universe's timeline but are eventually found out by Zen-Oh or the Daishinkan and erased. Without the battle with Zamasu, it could be that Goku isn't given the stimulus to achieve PSSB. If he doesn't, he is defeated before he can achieve UI and Universe 7 is erased. If he manages to do so though, things go fairly similarly in the ToP. Gohan may end up far weaker due to not having his potential unleashed, but Kefla would probably just be beaten by Jiren in that case. Without Boo, the Galactic Patrol instead come to Goku and Vegeta directly for aid but, due to underestimating Moro and not having Boo to help, Goku and Vegeta are killed and Moro's destruction of the universe goes unchallenged until Beerus sees it necessary to get involved.