Speaking for a dealer, they do not have to take the car back. Here is something to think about though, if you sign paperwork and decide you don't want the car, a dealer must negate the deal.
The purchased vehicle must leave the lot for a sale to be official.
Sorry to get off track. Make them fix everything, Buck. Check the mileage allowance on the used car buyers guide. Make sure you dont go over before all your issues are addressed.