I'm not so sure about video recording in a nursing home--it would probably depend in part whether your grandmother was OK with it, or whether she was competent to consent and/or you had legal authority to consent on her behalf. Those things can get tricky.
But someone's private home is a definite no-no, even if you have good reasons for doing it. You can understand why--stalkers use those kinds of techniques to monitor what their victims are doing. Even the police generally couldn't get a warrant to do something like that. And even in your own home, most places you wouldn't be permitted to video record someone without his/her knowledge. Imagine one's spouse who suspects you of cheating. How creeped out would you be to find out there was a hidden camera in the ceiling of the bedroom?