Even if her memory is poor, if she is capable of making decisions she would still be entitled to make a will. She would of course need to go to the doctor to get her decision making capacity assessed but just because you have a poor memory does not stop you from expressing your wishes and explaining your decisions. If the doctor thinks she has the ability then she should go to the solicitor and make a will. It will give her peace of mind and allow her wishes to be carried out.
Just because you cannot remember what day it is, or what you had for breakfast, or when you were born does not take away from your ability to know that you want to leave your house equally to all your children. If she is fretting about it now is the time to act.
Make an appointment for the gp, & the solicitor. Get a copy of your Dads will. Explain to both the gp and the solicitor that your mum is fretting about her lack of a will, that she has expressed an opinion that she wishes to leave the house to her three children equally and that she has memory issues. Let them take it from there and be sure to tell your siblings.