You may have trouble with "lives there for the rest of her life" given her condition - what happens when she needs 24 hour care and her son, understandably, cannot cope with that? You have an undertaking that she stays there for life, yet she won't have the mental capacity to argue about it and the person who represents her i.e. her attorney will be arguing with himself. As Canary says, you must have legal advice, but wonder if a a solicitor might have difficulty in advising both both mother and son together. Each will need to take his or her own individual advice and again, there is a have a potential conflict of interest with the son acting for himself and for his mother in this. Unless she has capacity to understand advice, or you as the other attorney can help her with that part.
If the son has to take out a mortgage to buy the property from his mother, the mortgagor will want to know who else lives in the house and what their rights are - might well cause a lot of difficulty if you say Mum has the right to live there for life.