My mom has BPD as well as me. When I was little she would have horrible outbursts and we struggled to communicate most the time. When I was little and was agitated with stuff she would try to distract me without feeding into my emotions too much. It would help so she wouldn't get frustrated with my frustration. I dont know if thats healthy but it worked for me and now me and my mom are best friends. Not sure if this is any help to you but I thought I'd share anyways just in case. I am sure you are doing the best you can. Parenting is hard. And having patience is hard.

As someone with BPD I find that when people have more patience with me during an outburst I’m more easy to calm down and I’ll apologize for whatever I did when I was angry. I also understand that that can be difficult when someone is snapping at you or trashing a room in anger. I’m sure you are doing your best to be there for your child and I promise having a person to rely on means everything. If you find yourself about to get angry and the option is available then take a second to step away take a few breaths and remind yourself that getting angry likely won’t accomplish much. This also gives your child a second to hopefully calm down a little bit.