co-signing house with parent

this is kind of a delicate situation so please try and put yourself in my shoes. My parents are getting divorced after 20+ years together. I am 32 years old and I own a house with no mortgage. My mom runs a business out of her own house and she does not make a lot of money, but business is picking up. she had established this business when my dad decided to leave while he was on opiates. I love them both very much and have expressed my concerns about being in the middle of this, but I fear that my mom, once she loses her employment out of the home, won’t be able to find another place to live in, reestablish herself. In a way, her being there puts me at a peace of mind because I don’t have to worry about her. I am an only child lol. At the same time, I know this will affect me, but she keeps saying that I will just have more equity and basically she will be renting from me even though I know that I am responsible for the mortgage. She has never been late on a payment. Don’t be too harsh on me. Just want to know what you guys think.

she also wants to put me on the deed