RC Car with Arduino Capabilities

Hey folks! I'm doing a project for school and have never used Arduino before, so this should be fun.

My team and I are looking to make an RC car that has the capability to switch between two battery sources and we were looking to use an Arduino to accomplish this. We have some coding experience but are looking for some advice on the feasibility of using Arduino for this project.

We're throwing around ideas of either putting the Arduino board in the actual vehicle or mounting it to the RC controller. Personally, I think putting the board on the controller is a better idea since if it's in the car the board will need a power supply that isn't coming from the batteries powering the actual car. However, I know nothing about how this might work and need advice.

One question we had was whether or not the radio signal would be able to transmit info from the Arduino on the controller to the car if it isn't mounted within the vehicle itself...thoughts?

If anyone has any knowledge whatsoever about Arduino in this sense or applying it to this project I'd love to hear about it!!
Thanks in advance!