Probably we'd be better served by me explaining why think it's a tangent: The issues related to who has the right to kill the baby have to do with harm done to people other than the baby. The core point I was trying to make was that killing a baby isn't inherently wrong in the way that killing an adult is because the baby isn't a person.

Certainly there are issues to be sorted out, in the same way there are issues to be sorted out related to who has the right to kill a pet dog. But if babies were people these wouldn't be important, relatively speaking: killing babies would be wrong for the same reason killing adults is wrong. As such I think they're tangential: unrelated to the question of "is it wrong to kill babies for the reason that babies are people?".

That said: The legal definition is probably adequate; barring that, perhaps we might say the parents are the people to whom responsibility for raising the baby would fall.