There is a concept called "betterment" that comes into play here. The insurance company is not liable to repair anything that was pre-existing before the accident.
In the case of rust, fixing the rust would be "betterment" and the claim denied. What they do need to do is return it, as much as is possible, to the condition it was in before the accident. Sometimes that is not possible due to the way the rust and the damage come together. The shop is not going to replace a rusted panel with a new one and then "rust" it so that it's like it was before.
Talk to your insurance company or agent and if you can't get satisfaction, talk to a lawyer. There is little else you can do which is why accidents suck. You rarely get made "whole" after one regardless of fault.
But in a case like this, you are likely on the hook to pay for the non-accident repairs which are now causing driving problems. The car was likely "on the edge" before the accident and it just got pushed over that edge due to the accident.
As an example, I was once rear-ended by another driver and this caused damage to the rear bumper, some trim, and the tailpipe/muffler assembly. They other driver's insurance company paid for all the parts and labor except for the muffler. They reason was that the existing muffler, though it was damaged in the accident, was rusted through. The existing muffler could not be re-installed because it was pretty much smashed. They did offer to pay for the labor to install a new muffler if I paid for the new one, which I did.