Who is the daughter, Cath, that Olivia will now never give birth to, really? What is her life like, having to deal with Olivia in a reality where she was too distraught to raise her? And why did she figure, after killing Ethan in all other possible realities, he should compromise with Tom, her old self, in what she knew to be the deciding reality? 
This the story from Cath's side, the badass version of the Rectifier that Tom would've become if not for Cath interfering with her alternate past to change it, and hence killing herself inside it in the process.
From her time inside the womb, where the heartbroken emotions of Olivia feel like they're poisoning her system throughout each term, Cath becomes a stronger, harder version of the Rectifier than she was when she was Tom. 
After she receives her second infusion at aged three, on what would've been Tom's fourteenth birthday, Cath tries to create a vortex to her past to change all that went wrong. With Mark's disappearance causing Olivia the most frustration, bringing an earlier version of him through may even allow for some loving emotions inside her, which could make her more receptive towards Cath.
It's only after she gets her dad, and is excited for Lucy to come alive in her reality after he goes back and saves her from her stepdad, Cath realises they've created a completely separate timeline. 
Thankful just to save people in one reality at least, even after her mum dies saving her life, Cath is determined to sort things out for Omnipion in the new past timeline they're creating. She may have the incline to kill Ethan in her reality, and all the others they viewed to get the scope on what worked and what didn't, but she knows Tom needs to compromise. Out of the thirty three they know, sixteen wins and sixteen losses, she knows his has to be the deciding reality.
The problem?
There were just two memories left to connect to, which she hopes to use in order to walk through into that new past reality and make Ethan listen to Tom.
The battle where Ethan either kills or banishes Mark.
The death of her old self, Tom, as he transfers his being into the embryo Olivia is carrying.
With half of Mark's being already in Omnipion, she knows she can only travel through at the first point and collect his dead body. Once she brings him back, she can place the plasma being she has on ice inside him, essentially saving his life. It means he can never travel back through the vortex again, however, but at least he'd be alive somewhere. 
At the second point, Tom will have already transferred his being, meaning she can extract it from Olivia's embryo, and place it back into Tom's dead body. It may kill herself in that reality, but she knew first-hand that losing an embryo was better for Olivia than losing Tom.
Can she make sure Ethan listens? 
She will threaten him if not! 
Will she also, in the time she will have left, communicate to Tom all he needs to know?
Cath may have been able to pull Mark through to her timeline, sending him back to change all she knew the original Olivia hated, but can she ensure Tom can create his own bridge to them? 
If so, the original mother she loved, who got to meet her in the flesh twice, could reunite with the only thing she will have now lost; Mark,
After all her hard work, and no more memories of the past timeline to cling to, all she can do is hope, with the information she leaves Tom, that he will, after gaining his second infusion, make it to their side. A hope to create the normal family life that version of Olivia always dreamed of. 
"MIDNIGHT LIBRARY meets SLIDING DOORS"