Actually, I believe it is the same Laura that pops up over and over.
S
P
O
I
L
E
R
In the 1897 story, Laura (Edwards wife) remembers Barnabas from when she was married to Jeremiah Collins in the 1700's.
Yup. But the whole Phoenix thing is very ambiguous. Let's look at the facts:
Roger and Laura marry. Laura gives birth to David. Laura goes away, to a "hospital."
Later, Laura is burned to death in a fire in Phoenix, Arizona. Afterwards, the immortal Phoenix is born from fiery ash. The Phoenix Laura returns to Collinwood with the intention of taking her son David back to her fiery underworld.
What isn't clear is whether Laura, pre-Phoenix, AZ fire, is the same person as Laura the Phoenix after she has risen from fiery ash. The same thing happens with Laura in 1897: she ran off with Quentin, who reported he saw Laura die in a fire in Egypt. Again she was apparently resurrected as the Phoenix. It seems as though she is born a mortal woman and the Phoenix Laura doesn't rise until after she is destroyed in a fire. She then has a small amount of time to reclaim her child before purposely burning herself again so she can be reborn the next century.
***
As for Joe Haskell, the family tree I saw does indeed indicate that Joe is a descendant of Quentin's daughter, the surviving twin Lenore. She apparently had two children, one of which married a man named Jennings, who was Chris/Tom/Amy's mother, and one of whom married a man named Haskell, who was Joe's mother. At this point, however, neither Joe nor Chris know they're descendant's of Quentin's.