A/N: So a supposed plot synopsis for the broly film has come out as of recently. I first got a look at it from UnrealEntGaming.

https://youtu.be/plvRhvUU7p0

So I then decided to track down the article he was reading from and I found it. 

(In case any of you were more interested in reading for yourselves rather than from the video).

So rather than fear, king vegeta wanted to get rid of broly because of jealously of broly's potential over his own son's. While this is different from the original reason, this is kinda something I can still see king vegeta doing. Considering vegeta and his father have been known to be rather prideful and he wouldn't want the child of another saiyan, even if it was a high ranking one, to overshadow his own son. Now, to add onto this, paragus' rank might be changed from a high ranking saiyan to a low class. Only time will tell on that when the film is released or further information. None the less, this does give us more to what's going on.