My sis is going through the same thing. I'm worried about potential episodes since she does not take her medication regularly. She needs a constant support system. You should assure your mom that you'll keep in touch and visit her as well. She means well. I know its stressful for both of you but it won't always be like this.
If you are an adult you don't need to prove anything. Move out. You have got this. PPD and PPA are temporary. If you relapse you contact a medical provider and do what you need to do.