I cannot answer the question about care homes, other than to say that travelling to and from the home to see his wife is clearly for her benefit, just as a carer travelling to and from work to provide an income to support a partner who is unable to work is.
The 5 mile rule is designed to stop abuse but is very flexible. My wife (the PIP recipient) can no longer drive. I was concerned that if I was away or in hospital my wife would be housebound and unable to visit me, so I asked Motability if I could add one of my daughters who lives 12 miles away. They didn’t bat an eyelid and were more than happy. In reality, she’s only driven it once in 18 months (and that was with me, so that she didn’t drive it for the first time in an emergency) but it’s reassuring to know that if anything happens she is able to.