As you enter the Soul Cairn, your first objective is assigned. You need to find Valerica.

Check your quest log:

Beyond Death
Serana and I have entered the Soul Cairn in pursuit of her estranged mother, Valerica, and the Elder Scroll she took when she fled Castle Volkihar.

Follow the road down. You can talk to souls along the way to learn more about this place. Kill a Boneman that attacks you on the way.

Keep going on the road south, and under some arches. Arrive at a big castle. There is a magic barrier blocking your way. You see Valerica inside. Wait for Serana to arrive. Speak to Valerica. She wants to know how come a vampire of mixed blood is in the company of her daughter. You can say:

I'm keeping her safe
I've saved her from your foolish plan
I'm just here for the Elder Scroll

Learn that Serana has sacrificed everything to prevent Harkon from completing the prophecy. But the scrolls are merely a means to an end. The key to the Tyranny of the Sun is Serana herself. When Valerica fled Castle Volkihar, she fled with two Elder Scrolls. The scroll you found with Serena speaks of Auriel and his arcane weapon, Auriel's Bow. The second scroll declares that the Blood of Coldharbour's daughter will blind the eye of the Dragon. Serana and Valerica were humans once. They were devout followers of Lord Molag Bal. Tradition dictates the females be offered to Mola Bal on his summoning day. Few survive the ordeal. Those that do emerge as pure blooded vampire. Such confluences are called "Daughters of Coldharbour".

Your options are:
The Tyranny of the Sun requires Serana's Blood?
Serana underwent this ritual willingly?
Coldharbour?

If you choose the second option, Valerica tells you that being selected as an offering to Molag Bal is an honor. Serana wouldn't have dared turn her back on that.

But choose the first option. Valerica says that is why she wanted to protect Serana and keep the other Elder Scroll as far from her as possible. Harkon means to kill Serana. If Harkon obtained Auriel's Bow and Serana's blood was used to taint the weapon, the Tyranny of the Sun would be complete. In his eye, she'd be dying for the good of all vampires.

Tell Valerica you would never allow this to happen, but she asks how exactly you plan on completing the prophecy without the death of her daughter. You can say:

I'll Kill Harkon
I need your help
Perhaps her death is destined

Choose the second option. Valerica says that she is a pure blooded vampire like Serana, and that her presence on Tamrial is as much of a danger as hers. Valerica thinks you see the Tyranny of the Sun as your chance at Deification, and like Harkon you won't hesitate to destroy anything that stands in your path. At this point Serana supports you.

After some more conversation, ask Valerica if she has the Elder Scroll. She says that yes, she has kept it safely secured here ever since she was imprisoned. Fortunately, you are in a position to breach the barrier that surrounds these ruins.