Most Helpful Guy
If he cheated just once, MAYBE he deserves a second chance.
THREE times together with all the other stuff you mentioned is just too much. I understand why your mom would want him back (breaking up/divorcing someone you have been together with for a long time hurts like hell, even if they cheated), but this goes way too far.
Be careful in the way you tell her your opinion. It is her decision in the end, but you can say that you have a very bad feeling about it and would rather not have him in the house anymore.
I wish you the best of luck!
Most Helpful Girl
She sounds like she has battered woman syndrome. Your mother's husband is toxic and she's an idiot for taking him back after he took not one but three other women into their bed.