I'm in Ireland so I'm not sure if things are similar but here we apply to the local council for equipment needed, the house is assessed by a liason nurse and it's decided what is needed, someone from the council comes out to agree on this and then you get 3 quotes from companies for equipment and send them off to the council, they pick one usually the cheapest and your (your parents) income is means tested as to how much you pay and how much the council pay, so for instance we got dd a stairlift, it had to be adapted to her needs and our house which came in at 4,500, we paid 500 and then you get the vat back a few months later.
We also have here where things like beds, chairs etc are done through her OT, these are paid on her medical card, dds bed cost 14,000, we didn't have to pay anything.
Does your parents have anything like an OT or a public health nurse? You can speak to them about getting equipment.
I know I'm in a different country but I have found that many systems are the same or similar to the UK.
Your mother may be afraid she can't afford specialist equipment, I know when I arranged things for my parents when they were alive, nothing was under a grand and they went without not knowing they could get help.
The thing with carers is, well I find anyway, when it's parents looking after the other, they feel asking for any help is a failure and they need to do it themselves. My own parents hated people coming into the house, could be a generation thing.
I think before reporting your mam, maybe check out what things are available to them. Maybe there's something that your dad can go to outside the house, your mam might be a little stressed and if there is any sort of day centre he could attend it would give them a break. Here we have things like arts and crafts and music and cooking and other things and a bus comes and collects them.
I went through something similar with my parents who were adamt they could manage and I have a severely disabled dd so am familiar with equipment etc