Hi,
By the time your buy two Arduinos, two joysticks, two enclosures and speed your time inventing a protocol to send data between them, this programmable 9 Channel 2.4Ghz transmitter and receiver looks like an incredible bargain at 54 Dollars. Its all you need for your current and probably many future projects at 54 dollars !
I have no experience of using it, but reviews look very positive and it allows you to get on with building the interesting parts of you project rather than spending your time solving problems which have already been solved.
As for connecting this to an Arduino, there is no modification required at all, you simple run a wire from the signal line (white) of each of the channels to an interrupt pin on your Arduino (not forgetting a common ground connection). Like this -
Its only a suggestion and I realize that as a hobby lots of people enjoy doing things from scratch even if there are ready made solutions available.
Duane B