Can a dealership demand that we return the car we chose and pick a different one?

A contract is a contract; once a contract is agreed to and executed between two parties, one party may NOT unilaterally change the terms--or cancel the contract--at least not so long as the other party honors its obligations under the contract. There are a few limited exceptions, which mostly involve--

* Mutual mistake: The first party thought the agreement was for A; the second through it was for B; but somehow what was written up as a contract was C, so that the contract did not in fact reflect the parties' agreement or intentions

* Unilateral mistake coupled with fraud: party 1 deliberately "tricked" party 2 into signing up for something other than what party 2 thought it was getting (e.g. "bait and switch")

* Impossibility, owing to events beyond either party's control--for example, the manufacturer no longer makes or sells cars with the specifications you wanted, so that the dealer can't  fulfill the contract through no fault of its own

But apart from the above, if you have fufilled your obligations under the sales agreement, you should be able to hold the dealer to fulfiling its obligations--i.e. you don't have to select a different car and can keep the one you bought.

Alternately, you can certainly offer to return the car in exchange for cancelling the transaction and you getting all your money back; but the dealership should not be able to compel you to take a different car unless something odd, along the lines of what is mentioned above, occured.