I got into a huge row on another thread for saying that I thought there was always a reason for this kind of behaviour, that laziness is not just a natural condition, and it sounds as if you too are giving a lot of thought to why they've ended up in this position. Which is lovely. But.
I DO think it sounds very much like a shared mind, that they just can't extricate themselves from the house, or each other.
If you're MIL is suicidal, she really does need to see her doctor. And maybe you could offer to go with her? Then you could outline the home life, if it's not already well known.
It is possible that all that trauma, on top of some neuro diversity/ intellectual issues, means that the men just can't make the leap necessary. If no one figured out the problems earlier, they're looking pretty entrenched in their behaviour.
The thing that really stands out is that they're sharing a room. Seriously, I cannot imagine anyone actively choosing that part of the situation, unless they're really... damaged? struggling with adult realities?
How long have you known them? Have you ever known them to have plans, ideas, their mum to ever have yelled at them to shift?!
I'm truly unsure what you can do to help, but MIL getting a second mortgage/ annuity would be a nightmare all around.
Before she was depressed, did she do everything for them? Has she stopped?
I wouldn't necessarily prevent my children seeing them, that's a very simplistic view.
If your MIL is pathological - wailing at her sorrows, "threatening" to end it all, no concept of what may be appropriate in front of small children, then of course avoid.
If she brightens up when she sees you all, and they have a relationship with her, then that's good, and the whole issue of hiding is also avoided.
Meanwhile, I grew up seeing sad relatives occasionally, as in lived in a boarding house, in horrible conditions, but as far as I knew, were fine the way they were.
At a very young age it made me very sure I never wanted to live like that.
There have always been petiole who weren't up to working, who somehow ended up staying home, completely lost what to do once their parents died. I'm not sure why we're all so surprised that this still exists.
But in the middle of all this you have to protect yourself. You have a difficult job, small children, etc etc. Listen to her, help her get practical support from others, but don't expect miracles.
One person with difficulties, possibly manageable, 3 adults with no real insight into their own situation? Zero chance of affecting change I reckon. Sorry. 