You can sell it for parts, but unless that's already your or your family's livelihood, it ain't worth it. IMO, take option 1/the check and let them deal with the car. They're going to turn around and sell it for parts, but let that be their headache.
www.kbb.com and
www.edmunds.com both list bluebook values of cars. When I totalled my Cherokee, my check was for more than either of the sites estimated--I guess they were more generous about the condition than I. Of course, you and they are basing it on the condition five minutes prior to the accident, not five minutes after.
It will affect your insurance if the other party doesn't pay. I don't understand the part about her not admitting--is there no police report. They don't hesitate to say who's at fault.