I feel for her but I never quite understand these situations because they stem from half-arsed conversations and compromises. I wouldn't ask him to move out, I'd tell him to. In a calm way. Just say, I love you but I am dying and have only two years to live. Since you moved in I am beyond exhausted because you make so much extra work for me, behave like a teenager and sulk if I pick you up on it. I want a peaceful calm life without added drudgery. And above all I love you and want our last few precious times together to be enjoyable not embittered. So move out. It's not working. Let's see each other a few times a week and love our time together. Let's make a plan for some things we'd love to do together. Move in with your dad so I am not using the precious energy I have left picking up after you and bickering with you. I am not asking, I'm telling you what I need. I only have two years left to enjoy being your mum and to enjoy the rest of my life and there's no point in spending them fighting.
People should speak kindly and honestly more often.