Actually they DO study domestic violence. When What's-his-name the KC Chief player snapped, I was able to point to statistics from their DV study in a debate. I also regularly point to the CDC studies. And find them less biased than the FBI, as the CDC calls it homicides, which theoretically include justifiable as well as criminal, while the FBI calls it murder.
As for more likely to kill a family member rather than an intruder, those studies SHOULD be funded, as long as they're scientific and reasonably unbiased/intellectually honest. And I wouldn't dispute that those likelihoods expressed are accurate. We are more likely to screw up than shoot an intruder. THat doesn't mean we shouldn't have them, just that we know we have to be careful and studies like that just reinforce the message.