Hi OuttaDaFog
Welcome.
I'm glad to hear your found answers to many of the issues around your life with your wife, her mother, and her sibling.
As any of you would probably know, during these cycles she would hate on me and tell me she didn't love me and would put down everything that was important to me.
Yes, many of us here know what these cycles can feel like for you.
I have been like a single parent for years, and most things around the house (cooking, cleaning, driving to appointments, housework inside and out, laundry, and most other household responsibilities) have been my responsibility, as she has refused to participate or assist.
You're not alone in this. Many partners of pwBPDs report having to do much of the "living" in the relationship. I too know what it's like to do the cooking, cleaning, housework, laundry, amongst other responsibilities while my partner lay in bed or refused to eat what I cooked for her.
(... .) I'd love some thoughts or advice, please.
It's good that you understand that it's difficult for her while you're going through all these things. It will help you when you're feeling angry about the situation you're in. It's also good that you're considering your children in your thoughts—in families with a pwBPD parent, the children often suffer without much of a voice.
For the emotional turmoil, what helped me a lot was to understand which feelings belong to whom. Yes, there's a lot of emotional turmoil in this relationship, yes, it often means we're supposed to be the big pillar of stability, but that doesn't mean we can't be clear about feelings and anxiety.
After you find some clarity here, it doesn't mean you'll use it in an argument, what it means is that it allows you to unlock understanding that will then make it easier for you to tolerate her turmoil. I know this to be true.
I hope you find continued peace and I hope to hear more about how your story develops.