Could it be dementia?

My mother has suffered from anxiety and depression for the last few years but now I'm almost positive that we have to add early onset dementia to the list.
She has begun to do and say things which don't seem to be symptoms of her anxiety or depression. Here are some of them:
She struggles to find the correct word for something and will use other words to describe it, for example, a toaster might be a bread cooker.
She has begun sneaking around the house, trying to find fault with things that I do. Last night, for example, I asked her to fill the kettle for me and switch it on so I could fill two hot water bottles. She did and then went upstairs. I am staying in the spare room which happens to be on the ground floor, so I went into the kitchen and realised the kettle wasn't full so topped it up with water and switched it on again. My mother rushes in to the kitchen and in the most passive aggressive way ever, looks at the kettle and says, "Oh that's strange, I'm sure I didn't fill it all the way to the top. Hmm how odd that I don't remember that. Unless you filled it up. Did you fill it up?" I tell her I did fill it up and then return to the spare room and wait for it to boil.mI then hear her in a very loud stage whisper, tell my father that I'm going to break the kettle, that it should never be filled up and that she needs to empty it immediately otherwise it will ruin the kitchen. This is a prime example of her completely overreacting but then talking about me behind my back. She then creeps downstairs (although I hear everything because the house is so old and everything creaks) and she goes into the kitchen and pours out some of the water. I catch her doing it and say, "Oh I'm sorry, was it too full mummy?", and instead of saying, "Yes darling," she stands there and lies. She says she was popping in to the kitchen to get a biscuit out of the cupboard. I asked her where the biscuit is and she says that she doesn't need it now.
I am living in a mad house and I don't mean that weirdly. But every single hour of the day is like the above example. She talks in riddles and lies to my face. She creeps around finding fault with everything I do and totally overreacts if something is not how she wants it. She cannot have a normal conversation because she lies about everything.
Just this second I asked to come to her yoga class and she tells me it's full. She can't possibly know it's full but instead of saying, actually I would rather go and do yoga on my own, which she obviously means, she just lies. It's not as if it's the kind of lie to protect my feelings because most of the lies are so nonsensical. They don't make sense.
So now, as well as the depression and the anxiety I have to deal with this strange behaviour. It is totally forgivable as long as she gets it checked out. But of course my parents are both in complete denial and refuse to believe there is anything wrong. I can't take it.