This seems to be a case study in co-dependency, with a big hook – innocent kids who's futures are being diminished by their parents' behaviors. While on on the surface it's apparent that the M.'s reasoning is disordered, it sounds like the husband is too much an appeaser, and perhaps feels too entitled or victimized himself, to offer needed influence. So, in the interest of helping the children, you are now being gradually drawn into the whirlpool where you, too, (and your resources) could get sucked toward the drain.
As clear as it is to us that the M.'s desires, choices, and consequences are the driving force, she may be completely blind to this. She's looking the other way, probably toward childhood needs of her own that always went unheeded. This kind of dysfunction is hard to address, especially by anyone outside the family. And especially anyone untrained in counseling skills.
I'm one of the "sensitive, sympathetic" people who has been taken in repeatedly, by family (I have my own history of dysfunction there), as well as by friends and acquaintances. And even strangers who come within my arm's reach, if they have a sad story, if they have a child or a pet who shouldn't have to suffer.
I've traveled that route at least a couple of dozen times in my 45 adult years. I may never learn how to avoid it altogether, but each time I learn a bit more. One thing that seems consistent is that these needy people almost always reveal who they are before I get sucked in, and I proceed anyhow, where angels fear to tread. People who actually can be helped by a boost from outside, and there are many, don't have that pattern of repeated failures and excuses.
Another is that there is something in me that needs to feel needed and heroic, and somehow believes that my input will count where dozens of others have previously failed.
And finally, if I really pay careful attention, I notice that I somehow believe that this time, my giving will absolve me of my own failures and heal my dysfunctions. These features are common to co-dependency.
And though my impulse may seem as pure as anything I can generate, it's still not coming from a healthy place. Dependent people count on people like me (and perhaps like you) to keep giving them whatever it is that will help them maintain their own self-deception, their own false expectations and self-defeating attitudes. It's not, ultimately, a gift to do that for them. While you hope to make a difference for their children or dependents, in the long run, it tends to just keep the family from hitting bottom longer.
While tragic, hitting bottom is what a person like this will have to experience before any meaningful change can happen. It's hard to watch, like a slow train wreck. And it's hard to watch children injured in the process. The good news is that at least some of the children will often learn profound lessons from experiencing this kind of descent for themselves, and learn how not to repeat this dynamic. And sometimes, parents wake up from the shock of realizing the ways they are hurting their own children.
I would look for county or public counseling services that are available to low-income families in many areas. They may qualify for that. And they may choose not to take advantage of the things that will actually promote change. This sounds like a family that only knows chaos, and anything more predictable may actually seem threatening.
I wish I could give you some magical advice, but looking on sympathetically while they live out their lives may be exactly what needs to happen. It's a variation on Tough Love.