Sad to say but it’s not unusual for a bully cat to find one cat and target that feline. The picked on cat also starts acting like a victim, and may as well be wearing a “kick me” sign.
I’d suggest that you act as though the two cats are strangers, and start with introductions from scratch. Set up a single room with all the cat paraphernalia--litter box, food bowl, scratch object, toys--and put the bully inside. Allow the mom-cat to continue to have free run of the rest of the house. Keep them apart for at least two weeks.
Start feeding the two cats on each side of the door. Use a sock to pet the mom-cat, especially her cheeks, and then use that same sock to rub all over the bully. This helps the two cats smell more alike. Cats that are friends lick each other and sleep together, and smell alike--so help these two cats start to smell more alike.
You need to build up the mom cat’s confidence. Offer more cat trees and hiding spots for her to get away from him. I really like the cat tunnels, so that shy cats can travel across a room out of sight of bullies. During these two weeks or so, the shy cat has opportunity to find the new places and stake her claim.
After a couple of weeks, open the door and allow the cats to meet again. Be prepared to interrupt any bullying behavior. Watch the boy cat for signs and distract him with a flashlight beam to get him interested and distracted in something else. If he does attack, stop the behavior with an aerosol hiss, or loud clapping hands--or simply throw a towel over top of him. Many more tips about introductions and dealing with cat aggression are in the book PETiQuette: Solving Behavior Problems in Your Multipet Household.