Sometimes you just have to work around it. They arent telling you to work, they are introducing minimum hours and income to claim, or you have to prove you are job searching, unless you meet the exclusion. If your own health is that bad you are saying you cant do shift work, then why cant you claim, and im not sure if its PIP or LCWRA, whichever is appropriate, so you dont have the work searches? Otherwise, one person meets the hour and pay requirement, and you just go to the odd UC appointment.
It sucks, but we, as a society, cant support someone choosing not to work, and not saying you are choosing this, but, some in society do. Therefore, benefits have to come with rules and exceptions, so those who can work dont just get a free ride. As a society, imposing this rules is better for everyone, as we need people working in all roles for the country t stay afloat.
Some times these rules are harder for individual circumstances. But unfortunately they cant be on a case by case basis, they have to be universal for everyone.
If you cant get LCWRA or DLA for a child, theres reasons for this, so you would then have to find a work around, either you get a smaller part time job eves and weekends, a WFH position, or, you partner takes on more hours to support you. These are your only options.
It may seem unfair, but its also unfair working every hour god sends to stay afloat and support your children, then seeing people doing nothing and living a better lifestyle. I personally spent 2 years working 60-72 hours a week, doing nightshifts, to support my family, when my now ex lost his job. I resented him for me having to do that. I resented people claiming benefits for no reason, and i feel justified in that resentment. People who CAN work, SHOULD. People who CAN'T work, we as a society should help them. Its that simple.