Hi and welcome! I am so sorry you are in such a difficult position. Like Turkish said, many of us have been where you are at so we can relate to the emotional aspect at least.
Even though I have done absolutely everything in my power to maintain a balance between my partner and my mom, it is never good enough for her.
I think this is important to take a look at. Trying to soothe your mom is not working. It is kind and even healthy to keep up with relationships outside of your romantic one, but that is different than what is going on here. You are aware that pwBPD (people with BPD) have a fear of abandonment so that is good. There is only so much you can do to support her through this as sometimes we end up feeding into that fear.
Do you think stepping back a bit and letting your mom learn to self soothe might work?