Ugh benefits bashers!
It's incredibly hard to claim disability benefits, in my experience it has been for the last decade. Certainly everyone I know has not been automatically switched to pip from DLA and I've just spent a month of 3-4 hours a day completing my own application for pip which I'm now nervously awaiting the result of.
I'm housebound agoraphobic among other things so couldn't attend an assessment and even a home assessment would be problematic at best.
In addition I hope you're not going around in real life telling people she's working 'cash in hand' unless you are absolutely certain that you are correct that she's paying no tax or NI and neither is her employer as accusations like that can close businesses. Being paid in cash DOESN'T necessarily mean it's "cash in hand".
Plus even if she's on ESA which is the income based/means tested disability benefit she could be working too as there's "permitted work" which means people on that benefit can work a little (there's a cap on hours/earnings) in certain jobs.
I've actually been discussing the possibility of doing some work myself with my advisor as a result of doing the pip form. She got to know me quite well as a result and has made some suggestions based on my work background and current circumstances and she's sent me some links to peruse including the permitted work guidelines
So before you malign this woman (who your husband at least must love whatever your issues with her) be 100% sure you have your facts straight certainly before opening your gob in real life.
It's really none of your business and you're likely only seeing part of her circumstances anyway.
Nobody apart from my mum, dd and best friend knows the full extent of my issues, much of which are very embarrassing nor does ANYONE know my full financial circumstances aside from when necessary bloody dwp it's nobody's business!
She may not be able to afford the heating on, another possibility is that depending on the exact presentation of the asthma, the damp and what type of heating it may exacerbate the asthma and THATS why she's not turning it on.
One place I lived it was supposedly central heating but it was these weird connected "blowers" in each room which really dried the whole place out and exacerbated mine and dds asthma. I ended up not using the central heating but getting a calor gas for the living room and halogens for the bedrooms. Hated it.
So check before you mouth off.