Vegeta is always angry, that's his thing. That whole Bulma thing isn't legit, she doesn't need to be slapped everytime for Vegeta to be strong - that scene was inserted for two reasons. 1: humour, 2: to show the fact that Vegeta is very strong now.
Goku wasn't keeping up with Beerus at all in SSJ 3 ~ he literally got shat on, and was no match for him. Vegeta actually got several hits in, and was hitting Beerus hard enough to inflict enough knock back to continue the barrage of punches. The past is the past, everything is always subject to change. If Tory wants Vegeta to be strong, he will be strong.
Actually now that you mention it, it could be that despite the fact that Vegeta does draw power from his anger, it is often replaced with fear, especially the fear of dealing with situations that escape his comfort zone. I did do an analysis on his character and from what I could deduce, is that he has a fairly low comfort zone. So when faced an opponent things go the following ways: Either everything goes his way and he is dominating his opponent, or his opponent is somewhat powerful so he forces things to go his way, by using his anger, brutality, bluffs and any other more unconventional means he can come up with, or none of those work, his opponent is too strong and desperation and fear quickly overwhelm him.
Now to me the scene where Bulma get's slapped has a somewhat more... well let's call it 'developed' meaning than yours. Vegeta does care his new home, his new friends, his wife, his family. So in that moment when his wife got struck, someone who means way more to him than he often lets on at this point in the story, everything I just mentioned up there regarding comfort zone, fear, desperation, left out the window. At that point he was fighting for someone other than himself, someone he cared about, who got hurt, making him tap into a potential that went far beyond his known limits at that time, stronger than SSJ 3.
Also read what I just said. I never said SSJ 3 kept up with Beerus. I said Vegeta became stronger than Goku. I mentioned the SSJ 3 form because at that time, that was his most powerful form.
Yes pure rage will bring Vegeta on top, but as we Tory has established several times in his shows/movies is that rage will only make someone incredibly strong, if it has a purpose.