OK, this is a hard question and not much is released about it till now.
Here's a short summary:
There are multiple characters in the One Piece universe with the letter D in their name:
Monkey D. Luffy, Monkey D. Garp, Monkey D. Dragon, Gol D. Roger, Trafalgar D. Water Law, Marshall D. Teach, Portgas D. Rouge and more.
In the Wiki, I found this:
Whitebeard noted that killing the bloodline of a D does not put out the flames that they (a person carrying the "D") carry and someone else simply will pick it up one day
So there, the "D" is linked to someone's name and not to the bloodline itself. So this would mean, you can't wipe out the will of "D". It will appear somewhere else in some other family.
Law said:
What's the Dark King thinking this time? The Will of the D. will almost certainly call up a storm again
and also the Gorosei mentions:
"D" means danger
So we can say this question is not surely answerable right now. But I'm quite sure this "D" is not just about bloodline. I agree that in the Monkey family the will is given to the next generation, but I don't think it's just about the blood, it's more than that.
Update: I also found a pretty interesting where "the will of D" could mean "the will to die". Reddit
Gol D. Roger, gave himself in the arms of death to inspire a new generation of pirates. Portgas D. Ace, fought for the honor of his captain and died saving his brother. Let's take a look at Marshall D. Teach. While fighting with Whitebeard he showed clear signs that he feared death. Minutes later we get a speech from Whitebeard telling us that he was not the man Roger is waiting for, and that he was also not a true D.*
You can find this in chapter 576.
At this point, Whitebeard speaks also about the "bloodline" and not just about the name. And you also never know how correctly translated this mangas are. I know its not a clear answer, but maybe you found some aspects which helps you.
