How do I know if my 81 year old mother has dementia?

My mother lives with my husband and I, needless to say, it is a difficult situation (they hate each other). I bought my home 20 years ago and my mother lived with me since that time and 2 years prior to (we rented the house I bought). I had my mother's name put on the deed in case something happened to me so she wouldn't have to worry about a place to live. I got married 5 years ago and of course, my husband moved in.
There are daily conflicts toward my husband from my mother over EVERYTHING!!!!!! She thinks because her name is on the deed that she is half owner and feels the need to control every situation within my home. She tells you how you are going to do EVERYTHING. Literally asks to be physically abused by physically challenging my husband. I could go on and on. Needless to say, this has put an overwhelming strain on my marriage. My husband and I love each other dearly, but the biggest dilemma I face is, "put her in a home" (guilt) or possibly choosing between the two.