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.
In this fanfiction, Goku has the potential to be stronger. He has mastered different forms like Super Saiyan and beyond. However, King Vegeta is not to be underestimated. He has his own Saiyan pride and power. If it comes down to a fight, Goku's adaptability and continuous growth in power might give him an edge, but King Vegeta's experience and strategic mind could also make it a very close battle.
In fanfiction, it's possible for Naruto to be stronger than Goku. Fanfic writers often tweak the power levels and rules of the characters' universes. For example, if the fanfic writer decides to nerf Goku's Saiyan abilities while enhancing Naruto's Sage Mode and all his ninja skills to an extreme level, Naruto could end up being stronger.
In some fanfics, Naruto can be made stronger than Goku. Fanfic writers have the freedom to manipulate the power levels and abilities of characters. They can give Naruto new and overpowered abilities that surpass Goku's. However, in the original canon of their respective series, Goku has extremely high power levels and abilities that are on a different scale.
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.
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.
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.