Your situation is quite similar to mine. I really feel for you.
My father had a stroke 10 years ago, this left him paralyzed and in a wheelchair. He has some movement in his left hand. He is of reasonably sound mind, but he is rather helples practically. He cant write, he cant wash, he cant make coffee, he can get on the toilet on his own, but not off the toilet. My mum was his carer.
4 years ago my sister and I (she lives in spain, I lived in London with my family) realized mum was developing alzheimers, and we decided I should move back home (to norway) with my family to be near my parents, and try to help them, and get them the care they needed, and hopefully sheltered housing. We estimated it would take us two years, and then we would return to London.
Well, my mum was going slowly down hill, they were both in denial. They were both digging their heals in. Mum refused to go to the doctors for assessment and to get a diagnosis, and dad supported her. I have had a 3 year long battle trying to get them to see their situation and get help. She was diagnosed with Alzheimers in June 2010. They were still adamant they were fine at home. Mum could not plan meals, she could not shop, she could not put groceries aside, she did not understand the concept of time, she changed her daily routine and started getting up at 3 am roaming the house.
Meanwhile my dad was in bed, unable to get up and go and check on her, you know, with being disabled, and paralyzed etc.
She was no longer able to care for my dad. She forgot meals, she forgot coffee, she did not care much about hygiene, did not understand sell by dates, and would think nothing of eating and serving green mouldy cake, etc.
My mum took a very sudden turn for the worse in January. Dementia is a cruel illness, it can take sudden downhill turns. It was like my mums mind had been like an elevator, going slowly down from the tenth floor, and then suddenly the wires broke at the fourth floor and she crashed to the ground.
She started hallucinating. Scary stuff. She saw devils, people shagging, people hanging laundry, my kids playing and mocking her, all in her own home at night. She suddenly did not recognize her home. She started packing to go home. she packed knives in newspapers, a fried egg, some herring, her glasses, some empty jars, etc, all in newspapers, taped together, and put together with towels in a bag. My dad then stopped covering up for her any longer. He was exhausted from listening to her going ons in the night, while he could neither sleep nor check on her.
My mum was sectioned this January. Today, she believes she is a young woman who has just had a baby, and she lives in a flat share with other people. She thinks my father has found a mistress and thrown her out. She is deeply distressed.
In my experience, the combination of a person with dementia looking after a disabled person can go very wrong.
Has your dad had a diagnosis? If not, this should perhaps be your first step, securing a proper assessment and diagnosis for your dad. This will make your position so much stronger when trying to get a care package that suits their needs.