So what's your question?
You're probably not going to find a ready-made shield that does what you want. You can easily enough cobble together some components and write some code to make it happen.
You mentioned the motor drivers were bad. You will need motor drivers for the Arduino to control. You could get a motor shield. How does the carousel know that 3 revolutions have occurred? I assume there is some sort of encoder or opto-interrupter to tell that it has made a full revolution? Or perhaps it is just time based and they switch on the motor for X number of seconds?
You'll have to find out more about the coin accepter to find out how it works. It probably pulses a wire to indicate a coin. As for the 7-segment display, you probably could run this directly from 7 digital i/o pins, unless it's more than a single digit or high current. If it's more than 1 digit, you'd need to use a driver chip or a shift register ic.