To gain trust you (and your mom) need to pair yourselves with good experiences for Ranji. Each time you pair yourself with an aversive (something he doesn't like) you are eroding all the trust you are so carefully building at other times. Your mom trying to get him to step up is an aversive. We know it is an aversive because Ranji immediately tries to get away.... it is escape/avoidance behaviour. If you can't stop your mom doing this, then I would leave the room so that Ranji doesn't pair you with the aversive too.
I wonder if you could get your mom working with you. Your goal right now is to do all you can to keep Ranji's body language relaxed... it might mean keeping a certain distance from him for now (apart from feeding and cleaning), it might mean getting down low (when feeding and cleaning), it might mean avoiding eye contact, it might mean doing silly things like singing and dancing on the other side of the room. If he is relaxed, then he will start pairing you both with that lovely relaxed feeling. BUT as soon as you introduce an aversive, that trust will disappear again.
With a bird that has a long history of positive reinforcement/good experiences with you, if you accidentally introduce an aversive, that bird will bounce back fast. With a new/untame bird which of course, hasn't got much history of good experiences/positive reinforcement, introducing an aversive means a HUGE loss of trust.... it takes a LONG time to build up that trust again.
For example, just over two weeks after Ollie my untame Amazon came to live with me, I had to towel him. All the trust I had painstakingly built up for those two weeks went out the window. He was back to being terrified of me. I had to start again, slowly and patiently gaining his trust again.