Can you tell us (with links) what remote control your using? Maybe the data transmitted is not serial and your lucky the bit patterns come through consistently at 4800 baud. When you Serial transmit the received data again your data will have start & stop bit(s) added so may/will never match what you received. Ideally you should try and grab what you receive with a logic analyser or scope. Maybe you could use Adafruit IR decoder Overview | IR Sensor | Adafruit Learning System to grab patterns if you have no other means or audio record it using audacity. Once you have the pattern then you may (assuming no encryption using rolling key) be able to decode and re-transmit it properly.