Here is a family tree of Desmond's ancestry (click on the picture to zoom in).
As you can see, the Auditore and Ibn-La'ahad sections of the tree are completely independent of one another (and their link is currently unknown).
It is not known how directly the Kenway portion of the tree connects to the others, so until future games reveal this link we will be unable to tell how well connected they are to the Auditores or Ibn La'ahads.
We can also see from the tree that the relationship to these ancestors is on Desmond's mother's side of the tree. So Desmond's father would be unable to use the animus to access their memories since he has no direct ancestral link to any of these families.
However, presumably any family member on Desmond's mother's side of the tree (from the generation after Connor to Desmond) would be able to access the same memories we have accessed from Desmond so far.
Hopefully the coming games of Unity and Rogue will help fill in some of these blanks on the family tree.