In my experience, it is a difficult transition to watch loved ones deteriorate from dementia. You have a person who used to have good judgement and thinking, but that changes as dementia progresses. I have watched my aunts and mother go through this, and I educated myself so I could be of more assistance. If, after sharing information with your family about it, they continue to believe her, there isn't much else you can do. You might explain to them that if she told lies about them, you wouldn't believe them! Right up until the end of my one aunt's life, my mother insisted that she was "fine," though she could barely see or hear and perform simple tasks. My other aunt needed 24/7 care and despite my urging, her sisters refused to do so, and it did not end well. Family can be very difficult to work with through this process. My father-in-law had to sit his in-laws down and mediate the care of their father, because the three were arguing and getting nowhere. Once he got through to them, they sought the proper care for their father. One other helpful tip is to speak to your mother's doctor privately and also possibly a senior social worker for advice. If you can get everyone on the same page, things fall into place better.
Tell them they need to spend more time with Mom so they can better understand what she is going through..