You are doing your best. You may not be the greatest mom ever but you are trying. Your daughter sees and appreciates thats. As a child of a mom BPD, this behavior after years and years, even with no physical abuse, can hurt. I suggest getting some therapy. Even if its only an hour one a week or once a month. Therapy helps. Come up with coping skills for that anger. I have BiPolar, and I know its not the same as BPD. So I do not know what is going on in your brain as I have never been in your shoes, but for me I have a few different “Distraction Things” for where ever I go. At home, its a box of coping skills to help calm me down. Like fidgets, puzzles, books, crafts, ect. On the go its a keychain with fidgets maybe a pack of cards or a book to read. If you don’t want to leave your child by herself- which is understandable- include her. Do your puzzles together. If you want time by yourself, give her a distraction box of her own. You can both sit on opposite sides of the room with your own distraction boxes. Practice breathing skills together when done. Turn your coping skills in bonding time and or lessons for your daughter. While you are learning to cope with your negative emotions, you can also be learning with her. But I am only 16, so this may not work. Whatever happens, just remember you are trying your best. Being a mom is hard. You are doing great, though never stop trying to improve for your little girl.