Please explain why the general definition excludes helping members of one’s family and ingroup. So far you seem to be saying you exclude them because the scientific definition includes them, which doesn’t make sense.
I wouldn’t say the scientific definition attributes any motive, it just describes what is. Certainly ants don’t defend their colony to the death because they think, “I cannot breed, so I must do everything I can to protect the colony so my mother can survive to pass on more of the genes that I share.” They just do it. In the same way humans don’t sit around calculating what percentage of genes they share with the people they might save (we didn’t even know how altruism developed until recently, so for most of humanity’s history this wasn’t an option, and even now that we understand altruism we would think it ridiculous!), they just do it. Certainly we think we’re doing it for other reasons—love, compassion, patriotism—but we wouldn’t feel these emotions if they had not been useful in engineering humans to act altruistically.
I have already answered this question from you once before, but you seem now to have added a twist. Before, your question was about a man saving his children from a burning building, now it is merely "helping" members of one's family. So since you have reworded you question, let me reword my answer. A person protecting their family is acting instinctively not altruistically. A person "helping" their family may or may not be acting altruistically, their motives would have to be examined to determine which.
Certainly ants don't defend their colony to the death because they think, "I cannot breed, so I must do everything I can to protect the colony so my mother can survive to pass on more of the genes that I share." They just do it.
They "just do it" because it is instinct- not altruism. If the ant could be altruistic surely there would be cases where the ant defended the beetle or the lady bug. (Yes, I know I am being ridiculous with this statement, but no more ridiculous than you speculating on the ant's reasoning process.)
(we didn’t even know how altruism developed until recently, so for most of humanity’s history this wasn’t an option, and even now that we understand altruism we would think it ridiculous!)
This gets to the bottom of why the science has a hard time with idea of altruism. The scientific mind cannot let something simply be what it is. They must dissect it and it must be explained rationally. While that may work for many things, it does not work for altruism. For once you have attributed a reason for altruism to be, it ceases to be altruism in the original sense of the word.