Hello and welcome ,
I feel for you and have been in a similar situation myself.
My mother in law (MIL) has undiagnosed BPD.
My Dear Husband (DH), whom I have been with for 11 years was once diagnosed with BPD and has since recovered.
4 years after I met DH, after getting off the phone from his mother, he tried to take his life. I risked my own life to save his. Whilst he was still in the ambulance and I was trying to manage my shock, my MIL called me and blamed me, saying it was all my fault. I apparently made him sick. Apparently he didnt self harm before he met me at age 30. It wasn't my fault that she didn't pick up on her son's own self harm at age 10! She was also quick to blame me to other members of DH's family, resulting in my FIL also accusing me on that same night and my sister in law cutting me off entirely.
I said nothing, just took the abuse and didn't even tell my DH (for a long time anyway) - I knew it was more important for me to help my DH and this 'blame game' from his family was only going to distress him further.
I concentrated on healing (luckily we lived no-where near them) and listening to specialists and eventually he received a BPD diagnosis.
As much as I understand that not all BPD sufferer's get BPD from bad parenting, in DH's case, all experts had no doubt that his BPD was the result of his early childhood upbringing and parenting he received as well as the fact his mother has uBPD (father also mentally unwell).
My DH and I knew the truth - that the persecutors were the perpetrators but we said nothing because there is absolutely no point trying to explain to this to his BPD mother. She would never accept it.
Eventually we had to, long story but my DH's mental health records ended up being subpoenaed in a court case and they stated in the family history that his mother had BPD and related his childhood abuse back to his BPD. Before my MIL was on the stand we decided to lightly tell her - it was met with denial and cutting us off entirely.
For years I just let her believe what she wanted so that my DH could continue to have a relationship with her (albeit a toxic one) knowing that she would likely cut him off if we told her the truth, like she'd done so many times in his life.
I find it hard to deal with her never ending bashing of her sister,
My MIL always had problems with her sisters and would often disown them for long lengths of time ensuring that her son also had nothing to do with them during these periods of not talking to them.
it's like she's projecting onto her sister the person she is.
My MIL was constantly projecting that I was doing things to her but instead she was doing them towards me
she lashes because I dare say differently than here and they she tells me I am purposely arguing with her,
My DH used to change significantly around his mother, always fearing if he ever said anything she didn't agree with, either her temper would come out or she would disown him again. Actually I was the same - walking on eggshells. This actually made things worse, because the more she got away with it the more she did it.
What helped me to get through it was understanding she is not a well woman and likely never will be and the only person who I cared about knowing the truth was my DH.
You say you speak to your mother every day. There are many skills on this forum site as well as books where you can learn the skills of speaking to people with BPD that can be useful.
You are not alone