The Beauregardes, unlike their chatty daughter, are quite a quiet couple. In fact, they don't even really make much of a scene until Violet's demise in Chapter 21. But let's start at the beginning.
When her daughter complains about her mom yelling at her too much (to a roomful of reporters, no less), and Mrs. Beauregarde speaks up to defend herself, Violet shouts, "All right, Mother, keep your hair on!" (8.5). So what does this moment tell us about Mrs. Beauregarde? For one thing, it tells us she's a bit of a pushover, and lets her daughter do pretty much what she likes.
So it makes sense then, that when Violet demands that Mr. Wonka hand over his magic (and unfinished) chewing gum concoction, the only warning Mrs. Salt can muster is "Don't let's do anything silly." (21.8) That's hardly the stern words of a strong mom.
And what does Mr. Beauregarde do when his daughter foolishly takes the gum? He cheers her on, shouting, "This is a great day for the Beauregardes!" (21.19). So far, Mr. and Mrs. Beauregarde don't seem to be the wisest parents around. They clearly don't understand the consequences of their actions any more than their daughter does.
Of course, when Violet begins to turn into a human blueberry, her parents have a proper freak out, and her father tries to get a little stricter, ordering her to "Spit that gum out at once!" (21.28). That might have been a helpful suggestion about two minutes ago, Mr. Beauregarde.
The last we see of the Beauregardes, they're hurrying off after their giant, blue daughter, and we never hear from them again. But we know one thing's for sure: if they had been a little stricter with Violet in the first place, they might not have such a blue daughter. Oh well. C'est la vie.