It often starts with a shock or surprise at the mpreg situation. Then, they gradually learn to rely on each other more. For example, Vegeta might start to show a more caring side that he usually hides, and Goku might become more responsible. They'll have to communicate more, sharing their fears and hopes about the future with the baby.
The fanfiction might make their relationship more equal in a different sense. Before, there was always a bit of a power struggle between them. But as mates, they have to respect each other on a whole new level. They would have to consider each other's feelings and opinions more. For example, when making decisions about how to face a new enemy, they would have to consult each other rather than just going with their own instincts like they used to.
His power would develop more in line with Saiyan traditions. He'd probably have a stronger base power due to the intense training environment on Planet Vegeta. There would be more emphasis on raw power and combat skills from a young age.
Bulma could be involved. Since she has a relationship with Vegeta and is friends with Goku, she might try to mediate between them when Goku snaps at Vegeta. She could be the voice of reason, trying to calm both of them down and make them see each other's point of view.
Vegeta would likely be arrogant towards Chibi Goku at first. He'd see him as just a puny Saiyan child. But Chibi Goku, with his innocent charm, might start to break down Vegeta's tough exterior. For example, Chibi Goku could offer Vegeta some of his food, which is a very Goku - like gesture. Vegeta would be taken aback but might slowly accept it. Then they could start to have simple conversations about their Saiyan heritage.
Yes, in the vast world of fanfiction, there are all kinds of creative and out - of - the - box stories. Some fans like to explore unusual relationships and scenarios, so it's possible that there is such a fanfiction out there. However, it goes against the original canon of the Dragon Ball series in many ways.
Well, if they were brothers in a fanfic, it could change how they interact with the other characters. Maybe they'd have a deeper understanding and fewer power struggles between them. Also, their family background and upbringing could be explored in new and interesting ways.
It's a bit hard to say for sure. Both Vegeta and Goku have their moments of strength. Goku has some unique powers and techniques that give him an edge at times, but Vegeta is no slouch either and constantly works to catch up and surpass Goku.