Remember that shops charge differently. Your neighbor hood talyer will be cheaper than a well known shop and casa. Paint and parts will also have different prices. Better known brands or original parts are always priced at a premium.
I was in a car accident last month. I insisted that they pay for all damages and that the casa will be the repair shop. The other party had insurance and agreed to it. Total estimate by casa is almost 80K. If it will be done outside, i'm sure it will cost less but they may or may not use original parts. Too bad that Honda is having supply issues and they are still waiting for parts for my car. Too bad I did not charge them for down time.
BTW, dont you have insurance? Your TPL should cover it. Or see if you have 3rd party property damage. That should pay for the damage to the other car.