I'm pretty sure Annie's mother isn't a Tybur, because narratively that wouldn't make any sense. We've never seen Annie associated with the Tyburs and the Tyburs are special among Eldians. They're treated like royals. They get to go to all the parties, rub elbows with dignities, and everybody instantly respects them.
From the flashbacks we see, Annie lived in a very rundown environment with a father who was extremely tough and her, and she was quite likely forced into the Warrior program to earn that honorary Marleyan citizenship, which would be completely unnecessary if she was a Tybur.
As for the spinal juice being stolen, we've never seen what spinal juice from a still living Titan wielder would do if injected in someone else, but I would guess nothing, because if that could confer additional power to any of the Nine Titans Marley would be all over like ants at a picnic. Also, this would mean that somehow her poor dad who can't even leave the Liberio internment zone without permission somehow got to the fabulously wealthy Tybur household, managed to correctly identify the War Hammer Titan (whose identity is a secret to everybody), and then extract the spinal fluid without getting caught.
It's not likely.
Marley refers to the loss of Annie's Titan as "the Female" and I believe it's called the Female Titan as well in Chapter 95 when they have a trial run of the new Warriors again another nation before sending them to Paradis. I don't have the chapter handy in front of me, but the Marleyan officers do a run down of every Warrior Titan's traits, including the Female.