Would Bulma have prevented Vegeta from going to the tournament?
It is clear that Vegeta tried throughout all episode of not showing how much he cared about the birth of his daughter, but it is also easy to think that Bulma had demanded him not to go to train for be present at birth, in the same way that she demanded that he be on her birthday (We know that She is the one who rules their marriage).
But it’s a curious fact that in Episode 77, it was Bulma who reminded to Goku that he was going to invite to Vegeta to train. Even, she didn’t look disgusted by the idea. (In adittion, she felt guilty and apologized for holding up Vegeta’s training in episode 83). And It makes me doubt that if Bulma really had prevented Vegeta from going to the tournament in the first place.
Which makes me think that like does Goku work in the farm because Chichi forces him, Vegeta uses to Bulma as an excuse to justify his “acts of charity” in front of other people, as if “she forced him to be more human”.
Maybe, also she demand him that he gives her affection (or to spend time together), so that she make believe him to be forced to do it, when in fact he wants to do it too.
And the only person who knows the truth is Bulma and she follows him in his game because he feels more comfortable, and she is happy with that.