Can a dealership take back your car after 2 weeks if they orginally qualified you but then couldn't.?

yes they can...you probably signed something that said "pending approval" and the bank said no thank you. Check your contract. In fine print it will give you a number of days that the dealer has to get your financing approved..if they go past that then it's their problem not yours. If not you have to give the car back or try to finance at a higher rate with more money down usually.