It's not that easy, most car fobs have rolling code security, so once the button is pressed the code changes. You need the official IC with the rolling code algorithm programmed in by the manufacturer and they probably won't give that to you. Probably the only way would be to purchase a second keyfob from the car manufacturer, and activate that keyfob via the arduino.
I'm not so sure about them using rolling codes. I've heard there are car thieves that have these "black boxes" that they can hold near a car and like magic the doors unlock. And it works with all cars too, not limited to a particular manufacturer. So it's not like they took out the crypto chip from an existing keyfob to use in their hacking device. Otherwise, it would be locked into working with only one brand of car. I think each car is programmed with a unique number (like a UUID, universally unique ID) that no 2 cars in the world share. When that serial number is transmitted using the proper modulation, followed by a command (such as "unlock doors"), the car reacts to the transmitted ID+command. I think these black boxes work by trying every possible UUID that could be assigned to a car, followed by the unlock command, using an ultra-fast dedicated microcontroller.
Of course, I could be mistaken about this.