Her mother
Do we know what happend to her mother? Did she leave or die? Claire mentioned she never knew her mother.
"I'd like to keep Spike as my pet"- Illyria, Angel S. 5
I thought that the home video that her dad watches in the Thanksgiving episode was shot by her mother. I seem to recall that the videographer says something like "Wave to Mommy." I'll have to rewatch that part to see if I'm remembering correctly.
If I'm right, that would mean Claire is lying about never knowing her mother. Young Claire in the video is very angry and won't smile or wave. I'm guessing that perhaps that is a sign that the abuse started at a very young age and Claire is mad that her mother didn't protect her. But, it doesn't explain what happened to her mom.
Yeah, it seems like it's her mother who shot the home video.
One other piece of evidence of her mother: In the Thanksgiving episode, when Claire takes out the pink baby ID bracelet from the ballet shoe box, there's a photo of her mother holding her (Claire) as a baby we see a glimpse of for less than a second.
I'm not sure, but I don't recall seeing a photo of her mother on display anywhere in the house.
It's too bad there won't be a second season (unless great word-of-mouth can help Starz reverse their decision): It could be interesting for the series to reveal what happened to her mother.