....and the inflammatory sexist statement, made without any proof, at the end doesn't help. Extrapolating from the timing (we have literally nothing else to go on) it looks to me that he wasn't fired for wanting to take care of his wife. Seems more likely he was let go for either lying (or "sin of omission") at the interview and then asking for special treatment when he turned up.
We don't know what the role was, so we don't know how likely it would be for evening/weekend work etc.. A company may well have a duty of care to its employees, but it does not have a duty of care to people who aren't its employees. Unless this was all nailed down at interview then the company didn't get what they were told they were getting. Sympathy for an employee is one thing and we don't know how the company would have responded to an existing employee suddenly having that need. What we're seeing appears to be a potential employee hiding something until actually employed and then trying to spring it on a company as an obligation.
I am currently at a company that has been extremely generous to me in terms of time needed at home. I would not expect that same generosity if I had turned up at interview asking for the same, and I certainly wouldn't expect it if I turned up without letting them know and then saying "surprise, I'm working like this now".