Soulcrystal
There would be absolutely no consequences even if Vegeta were to be outright killed the moment he gets to earth. Why do so many think that there would be adverse affects? What did Vegeta accomplish that was actually important to the timeline? Nothing! And the MC already knows everything future Trunks would have so I really don't see where the worry comes from.
Nah make him live Bulma. The mc is a training Junkie, and Bulma isn't. He will always be traveling so he won't really have time for Bulma. Some might say let her travel with him, but I don't think she will be able to support him, when he battle and get injure seriously and act as if nothing happen. Or when he torture himself under the gravity training room. Right now his training his god ki and he is close Godhood. Let the kai god girl be his women. And I really don't really want Vegeta to die. One of the reason Goku and him become so strong was because of their rivalry. And if he want to continue his road toward Godhood he will have to disconnected himself from the mortal world or make his friends and family immortals. Thanks for the chapter. more???