From what I've read, a lot of BPD triggers are learned in toddler years, where lack of permanence and inconsistent affection is first noticeable by a child. Also, I grew up an only child with 2 BPD parents, and am more along the co-dependent side of the spectrum, not BPD. It's a bit of a crap shoot which way any child can end up going based on parental "training". Some learn they can get their way acting out like the BOD parent, some learn their only source of affection is by being perfect at whatever the BPD parent wants at a given time.
And I think she is still too young to talk about "mommy's moods" and she has yet to face the brunt of her mother's anger - that has so far only been expressed on others, not on the children.
Thre are age-appropriate ways to open this up for discussion. Just remember that anything said to a child may be repeated badly to your spouse. I am sure she sees more than you realize, and is at a prime age to see you as pointed black if it suits mommy to do so, creating yet another hurdle for you to face.
I guess your best bet for helping stave off as much of the relationship-damaging behavior at age 8 is make sure your daughter can self-soothe. That she can understand that her actions have repercussions and other people have feelings too. That it's not okay to lash out at anyone no matter how angry you are, and that other people have a right to feel hurt if you do. That she is her own person, and while as a child she needs to listen to her parents, you can encourage her to be her own person as well. My BPD mother wanted a small clone to live vicariously through.
Maybe take some time and go over to the boards on here about coping with parents and siblings with BPD - see the stories there, and see how people have managed to cope, maintain relationships, and when needed, gone NC as adults.