Hi shell. A difficult one, but unfortunately not uncommon when it comes to care in certain nursing homes. I think a lot depends on why she is in the home and if she has any other conditions such as dementia of any type that would make her general care more difficult to manage. With the list you have given, and especially as she is very overweight, I would suspect that the care being given by the home is erratic. After all, she wouldn't be very obese unless she was getting a lot of unsuitable food, and I suspect a lot of carbohydrate rich foodstuffs, which will in turn push her levels up higher. I'm not sure how involved you are in her care, if you are, would it be possible to ask the home to arrange a meeting or call so you can discuss what has been advised? failing that, maybe her gp - they all need to be registered with a doctor.
If you aren't involved, then I'm assuming a social worker might be, you could raise your concerns with them. I wouldn't leave matters like this because it really does sound as if her care isn't adequate in some way, and needs to be reviewed as a matter of urgency.
Failing all this, you could try contacting the Care and Quality Commission (CQC) who inspect all homes, hospitals etc, and ask their advice.
Hope it works out ok.