CariadAgain It seems to me that you really do not understand the nature of dementia.
If someone has dementia, even in the early stages, the first thing to go is their capacity to reason. What you say to them and what they hear are entirely diffeent things. Anything you do tell them will have been forgotten as soon as you say it, or rather will not even make it into their mind at all. So talking to this lady about anything and expecting any rational response is, quite frankly, a waste of time.
The same applies to anything she says to you. her mind is in another world and she is living in a completely different reality. The thing is She cannot help it. Her brain is damaged, just as much as someone with a broken leg has a leg that is damaged and cannot walk.
The easiest way to deal with someone with dementia if they speak to you, is not to try to make sense of what they are saying or reason with them, it is just to listen, smile and make non-committal rmarks. Accept that everything she says is a reflection of how her damage brain is working and not rational thought. Do not think you can say anything to her that she will be capable of processing and understanding.
People with dementia often get angry because they are scared and frightened. They are dealing with a world they no longer understand, where things keep happening that they were not expecting and do not know what to do about. It is no different to our own reactions when we find ourself in a situation we do not understand - like for example your reaction to this lady with dementia. - You do not understand her, she is causing you problems and you cannot get a reasoned response from her - and this has clearly caused you a lot of distress and anger.