I'm not sure if there are really many publicly known 'real wife' stories about Kayden Kross in a traditional sense. She is more known for her work in the adult entertainment industry, but if we consider her personal life outside of that in terms of relationships, there isn't a great deal of widespread information on her as a 'wife' specifically.
Yes, 'Begum Jaan' is based on a real story. It delves into a particular era and the experiences of the characters during that time, showing the hardships and the spirit of the people involved.
Well, it has roots in reality. Umrao Jaan is believed to have been based on a real individual, but the story as we know it through different mediums has likely undergone creative alterations and interpretations.
There is little information available on Kayden Kross's'real wife' stories. Since she is mainly associated with her adult entertainment work, her personal relationship details, especially in the context of being a wife, are not much in the public domain.
Some specialty film and music channels might have it. You could also look on Amazon Prime Video or HBO Max. It might take a bit of searching around to locate it.