Physical & Emotional Abuse Support Group
Abuse is a general term for the treatment of someone that causes some kind of harm (to the abused person, to the abusers themselves, or to someone else) that is unlawful or wrongful. No one deserves abuse, period. Abuse can be emotional, physical, or sexual.

If cleaning distracts her...than join her in it. Make the "cleaning" fun.
Sounds like you have a close relationship with your mother. You can "celebrate" her life any day of the week, month or year. How about doing something to surprise her later this week, without your brother, and when both of you will be more relaxed and able to just have fun?
How do you know that he is "keeping her on edge".
From what you write in your other posts, you aren't close to your brother. So if he's got something going on at work where he has to be there, if he's got something medically going on (even could be his own anxiety/depression), it could be something with friends, with transportation, with a roommate.
You don't know.
And if his relationship with you is strained...he's not going to tell you. He'll probably even rather have you write it off to narcisim than to tell you the truth.
Even drug/alcohol addiction tends to be self-medication for mental health issues.
Quite frankly, I'm not sure if it's mentally health for any of you...to have him come. So maybe he's bouncing that back and forth in his head.
I'm NOT saying that he's some sort of victim here. FAR from that. Just that ...relationships are complicated.
That said, your mother apparently wants him there. And cleaning seems to be her coping tool. Joining her in cleaning is NOT doing something "for" your bother. It IS joining in with her..."being" with her rather than "telling" her what she should be feeling or what she should be doing.
That's why my opinion on helping her relax...is to join her. At the end of the day, if he comes, he'll go home. And your mother will still have a cleaner house to go to sleep in tonight.