Hit in parking lot

So I was at a mall and in the parking structure, a lady backed into my car trying to reverse into her spot. There was a witness and she knows she was at fault so we exchanged information. She said she wanted to do it outside of insurance and my damage isn’t terrible at all so I was willing to do that once I got an estimate for my damage. Now she’s being difficult and I no longer want to take the cash, I’m ready to report to my insurance. My only concern is if my insurance rate is going to go up? Sure she agreed that it was her fault to me, but once her insurance calls her, I doubt she would admit to them that it was her fault. I’ve also heard that regardless of the fault, both insurances still go up. I really want to avoid that because it truly was not my fault. Also, conveniently, she has now left the country on vacation and so her husband is the one communicating with me. On top of that, at the time of the incident, her insurance and registration that she showed me were both expired. Does that matter? What can I do?