A few other things to keep in mind with dealing with the dump truck's insurance company:

I would not mention that you already bought a new car. Just deal with getting the wrecked car fixed or replaced.

If they end up totaling out your wife's car, and they offer you an amount you're happy with, then you should also insist on them paying for the sales tax on that amount as you should not be forced to eat that when buying a replacement car. My wife had gotten rear-ended by a big SUV that totalled out her Mustang GT. They eventually offered a fair replacement amount for the car but would not pay for the sales tax that she would have incurred when buying a replacement car, so we kept rejecting their offer. They finally agreed to pay the tax as well.

And more importantly, i would not sign off on any medical claims (they usually try to either get you to sign that you weren't injured, or trick you into unwittingly signing off along with property claims). Don't let them off the hook for any possible future medical claims. Here in California we have TWO YEARS from date of accident to file an injury claim so they like you to sign off right away - don't do it. My wife thought she was ok, but almost a year after the crash she started having nerve pain in her upper spine then it moved into both arms (pain and weakness) and she had to go to a specialist - he asked her if she'd gotten in a rear-ender crash before. Turns out the impact caused a disk to slip out of place, then over time it moved further and ultimately pressed against a nerve. She filed an injury claim with the SUV's insurer which was initially rejected, but one letter from her lawyer and doctor got the medical bills paid.