Hello cars: Welcome to Psych Central.
Thank you for bringing your concern here to PC.
You wrote that you need some help & advice regarding your wife's behavior toward her daughter (your step-daughter) who was the result of rape. I don't know as I'm the best member here on PC to do that. But I'll offer you my thoughts regarding what you wrote. You mentioned you thought your wife must be bipolar or schizophrenic. I'm not a mental health professional. (Most of us here on PC are not.) But, personally, I don't feel you should jump to the conclusion that your wife has a particular mental illness. Mental health diagnosis is for mental health professionals. And my personal opinion is that we all toss mental-health-related terms around too loosely.
To my mind, the overwhelming issue here may well be that your wife was raped & bore a child as a result of that rape. This is a huge factor with regard to how she's treating your step-daughter I would presume. You didn't mention if your wife has ever had any kind of trauma therapy related to her rape experience. But, if not, that is the thing that really needs to happen here it seems to me. Perhaps as a part of that process, it will be determined your wife has one or more mental health diagnoses. But that is, it seems to me, more of a side issue at the moment.
Of course, assuming your wife hasn't dealt with the trauma she experienced, (& it doesn't sound as though she has even if she did receive some kind of mental health services at some point or other) there's no way you can force her to do what she needs to do in order to heal. As our host, Dr. John Grohol, Psy.D. has written: "Denial is a powerful Impediment to Treatment." However (again in my personal opinion) until your wife comes to terms with what happened to her, & how it has affected her since, I'm not sure there is much you can do to have a positive impact on the situation other than to continue to be a loving & supportive presence in your step-daughter's life &, perhaps, see to it (if you can) that she receives the mental health services she's going to need in order to repair the damage that has been done to her & will continue to be done until her mother is able to heal herself.
Here are links to 7 articles from Psych Central's archives. The first 4 are on the subjects of healing from sexual assault & the effects of trauma. Next there's a link to an article that discusses how to talk to someone who always gets defensive (just in case that's a problem you encounter.) Then there's a link to an article that discusses how to persuade your loved one to seek professional help. And lastly there's a link to an article that talks about how to help a loved one who is in denial:
Healing from Sexual Assault
Building Empowerment After Sexual Assault
Dealing with Sexual Trauma: 3 Phases
7 Signs Trauma Has You Stuck
How to Talk to Someone Who Always Gets Defensive
https://psychcentral.com/blog/how-to...essional-help/
https://psychcentral.com/blog/11-way...-denial/?all=1
My best wishes to you & your family. I hope you find PC to be of benefit.
P.S. Here's a link to DocJohn's article on helping a family member get help:
https://psychcentral.com/lib/helping...et-help/?all=1