. . . it’s easier to imagine your mom is two separate people than one.
OK, I'm not a psychologist, and I've never experienced DID. But I can think of an alternative explanation: your mom has different "personas" that she uses to her perceived advantage. Maybe when she's with people she wants to impress, she adopts a "fake" persona--possibly someone who is nice, concerned about others, giving, engaging. My guess is that this persona is mostly performative, to win other people's attention and/or approval. But maintaining this persona is exhausting for your mom. By the time she gets home, your mom adopts her "real" persona with the people closest to her--her family--with whom she can let her guard down. She doesn't feel she has to win you over, after all. Instead, she's focused on getting her family to over-function for her, cater to her whims, reassure her, do her chores, not leave her alone, always make her the center of attention, "prove" your devotion to her. When she doesn't get what she wants, she lashes out. She's constantly grumpy, irritable, critical, demanding, demeaning, controlling. If you dare to defy her, then she really throws a tantrum until you relent. She might project her internal dissatisfaction onto you, calling you a lazy, ugly, stupid, good-for-nothing, freeloading worthless piece of scum who will never amount to anything and would be better off dead. She might say she wishes she never had you, and that you ruined her life. That's all just projection, code for how she feels about herself. But she says this sort of thing so often that you might doubt yourself and start to believe her.
Sometimes though, when she's under stress, she'll show her "real" persona to those external people she wants to impress. Maybe she feels slighted by a friend. She'll throw some sort of tantrum, completely surprising her friend, because the tantrum is unwarranted. Afterwards, your mom will feel regret and shame. She'll pretend she "forgot" the entire incident even happened. That's just a ruse for avoiding responsibility and apologizing. If she's called out for her bad behavior, she might throw another tantrum and completely flip the script, blaming the former friend for some sort of grievance. It's mostly lies. She will DARVO: Deny, Attack, Reverse Victim and Offender. Internally, maybe she blames an "alternate personality" for this. But I think this sort of thing sounds exactly like BPD. PwBPD can't handle feelings of shame, and so internally they develop delusional thinking patterns and re-write history to make themselves out to be victims, instead of taking responsibility for offensive behavior. They'll deny any wrongdoing, and if they are challenged, they might say they forgot, or straight up lie about what happened. I might be off base here, but that's what I'm reading into your post.
Now, of course we all try to project our best selves to the external world. I'll try to put on a happy face when I'm at work or at a party. I'm not saying that this abnormal--I think we all do that to some extent, and when we get home, we tend to let our hair down and relax. I just think that pwBPD take this normal behavior to an extreme. The pwBPD in my life typically seems able to "pull herself together" to do whatever she wants to do. But good grief, her emotions can flip wildly, over seemingly minor things. One moment she seems happy, and the other, she's totally unhinged and flying off the handle. It seems to me that she can control her emotions for a short time, but she's easily overwhelmed by ordinary life. Many ordinary things seem too much for her, like she can't handle them. Minor setbacks seem like the end of the world. Minor stresses (a headcold, a flat tire, a parking ticket, an appointment) seem momentous to her, a reason to skip all other obligations for the day. Minor disagreements seem like reason to launch WWIII. She needs LOTS of downtime. She seems to have no stamina, no grit, no resilience. It's like ordinary life knocks her off her feet all the time, and she's constantly upset by that, because she feels tired, strained, incapable, overwhelmed. She thinks the world is conspiring against her, and yet she does precious little to deal with her problems. She'd rather rant and rot in bed. Do I have that about right?