Hi MeanLittleFace- ( love the name-

)
I struggle with a similar situation- an elderly widowed BPD mother who is alone at the holidays. Yet, when we do include her in family events, it is chaotic. She will get pissy over things like the wrong noodles in the soup, or the kids accidentally got something messy.
Do I have to call her?
No, you do not have to call her or anyone really. The question is harder than that though. It isn't about her but about you.
How will you feel if you do call her?
How will you feel if you don't call her?
What about the kids? What do they want? What example do you want to show them when it comes to treating parents?
These are not easy questions and you may feel ambivalent about them. By trying to sort them out, you can hopefully feel as comfortable as possible with the decision you make.
The first one is the terms of the relationship- NC, LC, C. Like you, I have chosen to remain in contact with my mother- which means we do call her during holidays. She lives a distance from us so we don't feel we need to visit or have her visit us- but we do call. I also send a gift at her birthday and holidays.
One idea is reactivity. Can we be less reactive to our mothers moods, feelings, up and down and just be consistent? This way, we are acting from our own decisions, not reacting to her. If we become reactive, then we are just drifting along with her moods. If we choose to act regardless of her, then we are in control of our choices. When my father died, I was so angry at my mother, I don't think I cared if I spoke to her at all. But I was not comfortable with NC. A very wise -older- friend advised me to call my mother at regular intervals- regardless of what mood she was in. I could choose that interval- once a week, once every two weeks. With regular calls, my mother knew to expect them. My calls were not based on reacting to her, but my own choices.
With what example to set for my kids? This was a hard one. I didn't want to teach them to accept abusive behavior. I also didn't want to teach them that it is OK to ignore an elderly parent just because they are difficult. For some families, NC is the right choice because the abuse is severe. In my case, I could deal with her- she didn't have that big of an impact on the family- I did protect my kids from her in ways when they were younger, but they aren't affected by her much. So, I decided we would call her on holidays and the kids would speak to her too.
This idea has been tested. My mother got really angry at us for something right before her birthday. I asked her if she wanted us to call and she said no. So we respected that. But we still sent a card and a gift. I don't know if she kept them or threw them out, but that wasn't the point, the reason I sent them was because I decided to, not for her reaction.
So, no, you don't have to call her. But also consider the idea of consistency vs reactivity. If you do not choose to go NC, a decision to call on some sort of regular schedule/birthday/holiday- no matter what her moods- may answer your question.