Here's another vote for not telling your mum. Just think about what you would achieve by telling her.It depends on the stage of dementia, but it sounds as though she is moderately advanced. She might not remember, in which case, she will suffer anew every time she is reminded, or she may become fixated on it, and the care home staff will have to deal with the consequences.
My dad is at the later stages of a vascular dementia, and he is still very verbal. My SIL has just died fairly suddenly. We have not told him. He did ask about seeing my brother "and family", when my SIL was in the hospice, and I said they were very busy at the moment, but they sent their love and would see him as soon as possible. He was happy to accept that. My nose might have grown a fraction longer, but he is content. By contrast, he is very upset every time he thinks about my mother, who died 26 years ago, and insists he has just found out. He hasn't of course.
To tell your mother will cause her distress, and with dementia, she hasn't got the tools in her mental toolbox to deal with it. It is an extra burden for you, but it is very probably in her best interests.