I think I'll just imagine a scenario with Raditz and see where it goes from there.
Chi-Chi would probably still try to keep Goku from training Goten, though I can imagine the latter sneaking off to secretly train with his dad, to his mother's dismay. So when the time comes to go visit Kame House, Goten would be forced to stay with his mother, while Goku goes with Gohan. By the time Raditz comes, the encounter is far more even than in canon, but given they don't Goten and Goku don't train together that regularly to avoid tipping Chi-Chi off of their activities, he still loses and Gohan is kidnapped.
Goten having learned to sense Ki by that point, has decided to go to Kame House despite his mother's protests to check on his father, but he won't arrive before they leave since he still doesn't fly as fast as the Kinto-Un. Things go just like in canon, except Goku and Raditz are both still weakened from their initial bout, to the point Gohan actually manages to knock his uncle out. Piccolo first kills him, and when he's about to finish Goku off too, Goten arrives and easily defeats him, though his father convinces his son to spare him.
This first part ultimately ends with them all training in order to prepare for Nappa and Vegeta. Though without access to Kaioken and Genki Dama, the fight against Vegeta would be extremely difficult even with the four's base strength being far above canon.
