No, it's not a typical trait of BPD. We'll generally inflict misery upon someone if we've been hurt by them, but it's most often aimed at the person who hurt us. We don't usually go around hurting others for no apparent reason, and not with that frequency.
Borderlines are very fragile people. If we were to accuse others of being crazy that often or talk about getting rid of them, we'd be deathly afraid that we might be putting the ideas in their heads to do the same to us; a twist on the self-fulfilling prophesy. Frankly, that's the last thing we'd want.
Whatever it is that your dad's going through, I hope he gets it figured out. It's obviously hurting you, and I'm sure it's hurting your mom and dad, as well, even if they aren't showing it. Nobody should have to wear headphones to protect themselves in their own home.