Hi Natasha27 and welcome to the group

So much of what you've been through sounds familiar, especially how your sister with BPD seemed to be triggered by medical events (your father) and life changes (your baby, your brother's baby) happening to other people around her. And, unfortunately it can be common for the pwBPD (person with BPD) to "take over" a certain family relationship and to act as a "gatekeeper", regulating who can and can't contact the family member, and using that to gain contact with or control over others. Your sister seems to know that you love your mother and want to spend time with her, so your sister plants herself at your mother's house -- trying to force you to choose "either both of us, or neither of us". I'm so sorry this is happening when it should be a time of joy with all the new babies in the family.
It sounds like your husband and one of your brothers are supportive of you, and understand how difficult your sister is? Is that close? It can be so meaningful when others close to us see the real dynamics, and support us in our choices to be healthy.
Minimizing contact with your sister would make sense. In the times, though, when you might have to communicate with her, there are some approaches that can help decrease conflict. For example, many pwBPD crave
validation, and when we validate others, we can help them feel heard which can help discussions stay calm and not explode.
Validation doesn't mean that you agree with her distorted view of the facts, or that you suck up to her, or placate her, or tiptoe around her.
Validation does mean that when she says something crazy, or wacky, or hurtful, or angry, you pause and think -- what are the feelings that might be behind those words? And then you respond only to those feelings, not to her false allegations or raging statements.
One example would be if she texted something like: "I can't believe you invited everybody else to your baby's party and not me. You hate me, and I'll never forgive you for this."
An invalidating response would be to try to
explain yourself to her: "But I didn't invite everybody else -- these other people didn't come. And I don't hate you! I just wish you could see that I'm trying to love you."
A validating response might be: "Wow, that would really hurt to feel left out. What's going on?"
You didn't have to agree with her blame and distortions -- but you found a feeling that she might be feeling, and agreed that feeling that way would hurt.
...
Would you say that your biggest concern if you were to avoid your sister and stop communicating with her, would be that she would "burrow in" to your mother's house so that you would have to avoid your mother if you did not want to see your sister?