a) The Mechaber in Shulchan Aruch (O.Ch. 567:1) writes, "On a Ta'anis, except for on Yom Kippur & Tisha B'av, one may taste food up to the size of a revi'ies if he spits it out."
b) The Rema argues and holds to be Machmir and not to taste on any Ta'anis even when spitting it out.
c) The Mishna Verurah writes that if you are cooking for a Seudas Mitzvah the night after the Ta'anis then one may taste it.
(even according the Rema)
1) Rochel is Sefardi who follows the Psak of the Bais Yosef may taste the soup.
Leah who is Ashkenazi must follow the Psak of the Rema and may not taste the soup.
2) Rochel & Leah are both Ashkenazi but Rochel is cooking for a Seudas Mitzvah after the fast.