I don't think you can connect an RC receiver into the RX and TX pins of your Arduino.
The RX and TX pins on the Arduino are used for RS232 type serial communication. It expects ASCII characters.
The receiver on an RC unit puts out PWM signals that are expected to be connected to servos.
I know the Arduino can generate PWM signals to drive servo's. It might be possible for the Arduino to read PWM signals as well. But I would have to investigate that. If it can, you would have to modify the code to read the PWM signals, mix them, and then send them to the motor shield in such a way for the motors to respond the way you expect them to.
This could be done. But it is not as simple as you are thinking at the moment. I think Shawn Hymel, at Sparkfun, made a series of videos on this very subject.
Also, I am intrigued by this project. My wife just mentioned yesterday that she wants me to build her a BB8. I recently got a Creality CR-10 so I could build a rather large body. But I see you are using a Prusa (Mk2 or 2S possibly). I have a Mk2S and a Mk3. I will probably use those.
THanks for sharing,
EDIT: I went and found the two blog entries Shawn made at Sparkfun.
Part 1: https://www.sparkfun.com/news/2462
Part 2: https://www.sparkfun.com/news/2463