Helen, what do the carers at the home have to say. If they say that Nanna is eating sleeping and responsive, then, despite what she says to you, I would not think twice about leaving her there. If she is crying all the time and losing weight then yes think about it, but first talk to your other family and to her GP. It may be that she is clinically depressed.
You know, deep down, that the reason she and you sought a care home in the first place, has not gone and that dementia is insidious. It creeps along and then jumps out again when you have been lulled into a false peaceful state.
Do look at the posts that Isabella41 put on here. Her Mum desperately wants to be at home/sheltered/EMI unit/ Southern Ireland, but truth to tell is not happy in any of these places, because the home she wants does not exist....at least, not in this world.
My Mum has been in the CH for 10 months now and for 8 of them she thought it was a big mistake....for most of the last two months, it has now become a way of life, but, I do not kid myself that her want to be somewhere else may flare up at any time. However, as long as she is safe and well cared for, the CH is where she will stay.