If I were in the OP’s shoes, I’d talk to a lawyer who specializes in automotive issues. If you receive a settlement to compensate you for the damage, you might choose not to get if fixed if you can confirm from body shops that it isn’t dangerous.
If the lawyer and body shop confirm that this happened because the car is old and rusted, you might consider that this car is too unsafe to continue using.
at first, it sounded like a clear case of auto shop fault. but as you present the idea that independent body shops say this is what happens when your car is in this condition, it kinda leaves it open that maybe the tire shop was doing their best, as maybe the jacking rail was not useable and he used another unrecommended area.
if that is the case, they should have asked first, but overall it may say that your vehicle is not in great condition. asking for replacement or damages may be a little harsh. verify the cond of your vehicle and go from there.
if you make a small company pay for denting a rustmobile, that may not build great kharma.
If the age of the car is a factor, that doesn’t mean the shop wasn’t at fault. They damaged your vehicle. If they knew the age of your vehicle was an issue, they should have been more careful. If they didn’t think age was an issue - and it really was - they were negligent. It doesn’t matter what people at the body shops said.
If you want to attempt to recover your damages, you should go forward with this. If not, that’s fine too.