You said it was a big name dealership , so i'll assume they have a few car lines they sell from different manufacturers, and a history of being in that community. Depending on the size of the company , they may well have there own 'in-house' body shop, in a building owned by them, with bodymen and painters, [and a spraybooth] on their payroll. Or if not, they likely have a long standing relationship with an independently owned place that they trust to outsource their work to, which would be a significant chunk of that shops business annually.
As long as the VIN # is specified on the contract you have , you should have no worries. I would expect to pick it up in good condition on the day specified.
Did you actually leave a cash deposit , or supply a credit card # for a deposit ? If so it would just make your case go better if something went awry.
I have heard of cases in the classic-car-world where a seller backed out of a contract, and the buyer sued sucessfully for "loss of opportunity", [ based on what profit the buyer might have made if buyer re-sold it to a 3rd party - ie; seller offers collector car underpriced at 10K, makes contract with buyer, seller refuses to complete transaction, buyer proves to judge that he could have re-sold for $20K based on a predominantly accepted real market value, buyer is awarded maybe $5K]
Alternately , if you had to rent a car , because they were late on delivery , maybe you could get a weeks rental reimbursed, but if you had to go to court for that, would it be worth the time and filing fees to win maybe $250 ?
If they just sold it out from under you in a case of sinister subterfuge, than maybe you'd be pissed enough to go to court, on principle alone...
It sounds like you are carless at present anyhow, so if it were me , and they were 2 days late because of "work backlog" , i'd just ask for $100 credit with their parts department, or a couple free oil changes to compensate you for the inconvienence.
Really i think its just a bit of anxiety, having to wait to drive away with it. Don't stress on it. They are going to fix the car, it's common to have a " we owe buyer such and such" situation. They want to sell you another car in 3 years.