Hi WizerNow , and welcome to the family !
How do I stay calm and remind myself in the moment what he's doing reflects only on him? How do I not take the bait to engage him and stoop down to his level? I am good about it most of the time but when his responses are so off the charts I feel if I don't push back he will spin further out the next time.
Everyone has their own buttons. Over time, your BPD partner will become an expert in pushing them. That's why it will be so hard to stay calm.
In this particular situation about their mother's appointment, I would probably not be angry at my wife's overreaction. But when I need to have a friendly talk about the scratched pans in the kitchen and she blows out at my face, it's so hard to not react. Because I value my pans, but they always get scratched, and I feel like I have the right to have my pans preserved. This is my expectation.
So in the end it's all about your expectations being broken and perhaps your needs not being met. Maybe it would be helpful to write down your expectations and needs. That will bring you clarity about the core reasons for your frustrations. It should include all of the good things you expect from him as well.
And then perhaps if you want to take another step, then you could try to talk to him about your list, pointing out some of your wishes that are being fulfilled and some that aren't. When approaching him for the first time, select just a few items from your list. The first ones should be items that are being fulfilled. Then in the end you add one or two that aren't. If that doesn't go well, just give up and keep the list for yourself. It will be helpful to guide you in your decisions.