I think some people are married to their misery. That can come from depression/anxiety/fear, and it can come from self-loathing. Sometimes the bad habits we are in are strangely comforting. Depression can make people really feel like they're in quicksand - they may try to move, but they just can't make progress.
Some would say she's getting a payoff of some sort from her unhappiness, whether it's because she likes being a martyr (I'm not sure most people feel this way, but some do) or because the complaining is such a part of her make-up at this point, it's just all she does and all she knows. You say she can't really move out and break up - that can be financial or emotional, or both. I would say absolutely NOT to consider having her live with you. Depending on her age, she may qualify for low income housing but the waiting lists are long, and you would have to convince her to investigate and sign up with no guarantee of an opportunity for (sometimes) years. I do think you can contact her doctor or therapist and make sure they are aware of her behaviors - they can't talk to you without her permission, but they can listen to you. (Might be better if it came from her son though.) If she's amenable, a separate meeting with you and your husband with the therapist might be good, or a combined one with her in attendance. But she'd have to feel it was going to be helpful to her in some way to bring you into that circle.
If she's not getting anywhere with meds or therapy, she could try another person. But my husband's cousin is a good example of someone who just can't beat the disease - he has a severe personality disorder, depression, OCD, and really is locked into this mental hell for the rest of his life. Sometimes we just can't fix things for people and we have to quietly, painfully, helplessly let go. I'm sorry for you and I'm sorry for your kids too. Just keep the visits brief so that her negativity doesn't overwhelm the kids especially. But it does sound like those are some happy moments in her life so try to continue them if she doesn't say negative stuff to them.