It's enough to drive you insane. How do others deal with toxicity at her level?

I wouldn't be in the general area of any toxic person, no matter whether or not they are a relative. Life is too short. They would be on their own in much the same way they would be on their own had they never had any children.
You have chosen to stay and to help. It is a certainty that she will not change. And I cannot imagine it will become at all easier until you accept that fact. Expectations of change should be over with.
Let your Mom know that these are the things you will agree to do. That when she needs more care she will require placement; that you cannot ever do more, and that living with you would never be an option. Let her know that you will not abandon her, but that you will not often stay with her, as her habitual negativity has a bad affect on you, and your first obligation is to yourself, your own life and immediate family.
Your Mother's general condition (as an old Nurse I consider the end stage of COPD to be one of the most dreadful thing know to man) physically will not improve her general depression, and the side effects of meds given for this condition, steroids and etc simply shred one mentally and to the BONES quite literally. Don't expect a whole lot of "happy happy" out of someone suffering to this extent chronically.
I am so sorry for your Mom's torment, and for your own as you attempt to give her some care.

Perhaps start having her groceries delivered, and set up televisits with her Dr's when possible to cut down on the time you have to be around her. Being around such toxicity can be very hard to handle for any length of time, so really for your own mental health's sake, you must start limiting your time around her. When she starts in on her "pity party," you tell her that you must go now. It sounds like the day is coming(probably sooner than later), when she will be needing more assistance than you will want to provide, so you might want to start looking into some assisted living facilities now, so you will be ready when the time comes. And if it's not already done, make sure that someone has her medical and durable power of attorney, and that she has all of her end of life wishes known as well in the appropriate paperwork.(living will etc.) Best wishes.

You put up boundaries. If you don't know where the boundaries should be, please see a therapist (many people do and get great help). Her care situation will be tricky with the language barrier but that's not your problem, although I understand it feels like it is. It isn't. May you receive peace in your heart as you put up protective boundaries.