How can I convince my mother to live with me so I can take care of her?
Your mother is indeed young to be diagnosed with dementia. Many studies show that depression may be a strong link to dementia. It is vital to have have treatment for depression and good follow-up.
If you are worried 24/7, work with the neurologist to help your mom move to a safe situation. You might say that until you she is feeling better, your doctor feels that you should live in an assisted living community or with you. Always leave room for hope such as saying when you get better, you can go back home if that is what you want.