Idk if this has to do with BPD but I don’t believe my mom sees me as an adult. Rather she seems me as an extension of herself. My husband and I share bills. We’re both adults. However, to her, our home is only my husband’s home and I just live in it. I think this may be narcissism.
That rings true with the people in my life who have BPD. I don't think there is a sense of "self" strong enough to see others as separate. The closer you are, the less likely people with BPD may see you as separate people. Many pwBPD have no defined beginning or end so you don't either. You're the same person. Since she doesn't know what it feels like to have a defined sense of self, she probably doesn't understand what you experience, which is having a sense of being separate from her. It would make no sense to her.
It’s awkward when she comes to my house and there’s a tension in the air. My life now feels like it’s her, my baby and me vs my husband my baby and me.
I have something similar with my adult stepdaughter. There is almost always tension, and when there isn't, I don't trust it will remain that way.
Your mom probably feels some kind of fusion with you/your baby that she cannot make happen with your husband. People with personality disorders have a tendency to "split," which means she sees people as all good or all bad. It's a developmental stage we go through as children. People with PDs don't progress from that stage and learn how to see people as a whole, where good people can do bad things or vice versa. If a person does something they don't like, that person is bad. Period. If a person does something they like, that person is good. Period. Your mom probably sees your husband doing things she has no control over, which makes her feel bad, therefore he must be bad.
Right behind splitting is drama triangulation. If someone is split "black" or bad, your mom will try to enlist you, and because she sees you as an extension of herself (as well as your baby), you must see your husband the same way.
The tricky thing is that if she is seeing pink unicorns and rainbow zebras and you don't, telling her she's wrong leads to conflict. When my stepdaughter tells me someone is a pink unicorn, I try to stick strictly to validating questions. She is dating someone she's loved then hated then loved then hated then loved then hated. They break up, get back together, break up, get back together. In the interim, he is terrible, horrible, awful. Then he is sweet. Then he is horrible.
I listen and nod my head. Sometimes I'll say "Oh?" Or "wow." "Ouch." "Huh." Or, "What happened next?" But that's rare, because I don't ever want to hear more

Some people on these boards have some success improving the emotional regulation of their BPD loved ones, but that seems to work best from parent to BPD child, or from BPD sibling to sibling.
Being married to someone with BPD (especially with kids involved) or having a BPD parent (where you are the kid) seems to engage a different degree of boundary setting, probably because kids are involved (either as an adult kid, or having grandkids, or raising kids).
It might be more helpful to apply skills that help you manage boundaries so you can have a healthy emotional distance when your mom is thick in the deep of BPD behaviors.
I make sure there are a lot of activities when my stepdaughter visits. I limit my time with her. I protect my inner emotional life. We try to arrange visits that includes my stepson so it's a foursome. When it's me, SD26 and her dad, the tension is exhausting and the manipulation is feels almost toxic, like I'm a second wife or something.
Unfortunately, I don't think you can eliminate the tension, only mitigate it and manage it. Her wound is not visible, but it's a wound nonetheless and it's part of her whether she acknowledges it or not, whether it's discussed or not. All that matters is that you know it's there, and that it impacts your relationship and how you interact.
When you love someone with BPD, it's essential that you recognize you're the emotional leader, by default. You're able to regulate your emotions and see people separate from yourself. That's a huge advantage! It took me a long time to not feel resentment, especially after surviving a BPD sibling and then marrying/divorcing a man with BPD. I am so very very tired of BPD pathology.
Sometimes, the best thing to do is grieve. You have a loved one who is mentally injured and that can feel like a lot of responsibility, especially when the natural roles are reversed and you feel like the parent, and your mom the child.
I'm only now beginning to come out of a long stretch of resentment, and even then, it's always right there within reach, a very easy place to return to. The silver lining is that it has pushed me to be very good at taking care of myself, and in learning about BPD, I have become a much better parent to my son, a better friend, a better wife, a better manager and colleague.
There are upsides to loving someone with BPD, although it does take quite a lot of work to see those benefits and even then, the benefits may not be fully evidence in the BPD relationship as much as in other parts of your life.