Your issue is with HER. Not Geico.
Geico is her insurance company (or not...) but either way, she is the one you have a claim with.
A lot of folks feel obligated to deal with the offending party's insurance company: you don't. They aren't your provider and you have nothing to do with them. (except for those weird occasions where both parties have the same insurance company...)
Sue her. It's her problem to either figure out how to make you right, or to get her insurance company to step up.