She sounds abusive and a class manipulator. She just hasnt taken any ownership and let it all out through her DD.
What i would say is the reason she let her dd keep going to the club was because you were offering the lifts. This meant her dd got more invested in the activity. It may be that this is about the lifts issue (your friendship/practicalities) for you but for her its about her dd's being dependent on the activity. She cant stop her going. Her dd has possibly expressed she doesnt want to walk, or asked why she cant still get the lift, the dd may have past form for getting upset over friendships, worries about rejection and so on, and your friend hasn't explained...
I think you probably could have been more explanatory in the beginning, just in the sense of saying you are giving 4 weeks notice, as unfortunately you have too many commitments. That would have given her time to find a solution.
Whether she wants her dd to walk to yours or not is her decision. You cant know the reasons why she doesnt want her doing that. For me i would worry about doing the same route regularly in the dark as you can get followed. So to get cross with her for not wanting that solution isnt really fair.
I think you have to let the past lifts go in the sense that you gave them, its done.
I dont think your friend is thinking about your friendship at all right now, she is more concerned about sorting out the practicalities. So all the stuff about your friendship is going to fall on deaf ears. She is very unlikely to have empathy for you right now. Maybe she will harbour a grudge I don't know.
By the way I am sounding like I am siding with your friend, I am really not!! You literally have done nothing wrong.
I do think maybe try and give this less of your emotional energy and maybe let it blow over for a while. Dont be drawn into the drama or tit for tat.
Also another thing I thought of is that its really important that your DD sees you being assertive and standing up for yourself as she will remember that. Your Dd sounds amazing.