I don't know how it is in your situation but saying something to my BPD mother isn't effective and her response is to minimize it. If it makes any difference- my BPD mother still doesn't "listen" to me but to describe it- she doesn't perceive "me"- the "me" that is an individual and also boundaries.
What I see your D saying isn't a complaint or over complaining. She's 12- she perceives something but doesn't have a way to express it. "Mommy doesn't listen to me" is her way of saying her mother doesn't perceive her as an individual with her own needs and feelings.
Asking for time to do homework isn't an unreasonable request. What your D is saying is that she cares about her school performance and needs time to work on her assignment. Her mother isn't just not listening to her. She is dismissing something important to your D. She is choosing her own wishes over those of her D.
This is the shift in the relationship with a teen child. The teen is becoming more autonomous and the parent needs to be discerning about when to let go and give them some more self direction. This depends on the request and their behavior. If your D watched TV instead of doing homework- then she isn't ready for the concession, but it sounds like your D is doing homework- and this is a reasonable request. If her mother didn't feel like cooking dinner and wanted to go out to eat- she could instead change course and order take out- win win for both.
It also seems that this isn't a one time thing but often- BPD mother taking the kids out instead of staying home where D can do homework and so this could be more problematic.
Younger kids are less autonomous and so have to do what their parents choose for them. Teen begin to make their own choices but still need parental boundaries. The parent shouldn't give them too much autonomy but also not too little. It's not always clear how to navigate this. On your part- hear your D out. If she's truly finding it hard to do homework during her time with her mother- how can something be worked out so she has this time?