It sounds like your claim is well within the $10,000 maximum for claims in small claims court, so if the lady's insurance company is not dealing with you fairly, you can sue her (not her insurance company) and ask a judge to award you what you feel you are entitled to - they will then have to pay that amount. There are a number of guidebooks online to help you present a small claims court case for damage to your van, and also there may be an assistant in the courthouse to help you fill out the paperwork. Best of luck.
Depending on the insurance company, some companies will give you the fair market value, minus a minimal amount, if you wish to keep the car. You also have the opportunity to present the claim to your own insurance company, and see what they're willing to pay out. They would ultimately be reimbursed by the at-fault insurance carrier.
I assume you have no co,llision coverage of your own. If you do, you can see if your co is willing to repair it. When a veh is damaged the deft is responsible usually to repair it to the same condition it was in before the crash. if the cost to repair is greater than fair market value, the veh is totaled. Then they owe the fair market value. That value can be be diputed. You have the burden of proof as the claiminat. Normally if they pay for the total loss, they get the pink slip and own the veh. They sell it for salvage. They should have a salvage bid. Usually they will agree to pay you the fmv less the salvage bid, and you keep the veh. It will be reprted to dmv as a salvage veh which can affect the title and future resale (which appears unlikely if you plan on fixing it and keeping it til it "dies."
You are entitled to obtain the fair market value of the vehicle, or the cost of repair, WHICHEVER AMOUNT IS LESS. You may think it is a fantastic vehicle; much better than cars 10 years newer than yours, but the reality is that with extremely few exceptions which you do not seem to meet, a 1996 van, being 16-17 years old, is not going to have much value on the open market. $800 difference between what you say the cost of repair is and the carrier's offer may not sound alot, but unless you can show vans of the same age, make, model, etc. as your are getting higher valuations than the "totalled" price the carrier assessed, the liklihood is that you are spinning the proverbial "wheels" by trying to get more - consider the cost in time and money if you want to litigate this.