Man, I'm not sure robotics is a way to deal with depression (bit bipolar, myself). Always find it's a bit of a letdown when the project is done, and it's "ok, now what?". I'd suggest a dog.
But having said that: if you already have the mechanical bit built, and it's just a matter of sending 5v to output pins in a sensible sequence, then of course this is all very do-able.
What I'm getting, however, is that you haven't quite nailed down what you want to to do. You want it to be wireless controlled, and at the same time you also want it to be autonomous. Oh, and it should also have a switch operated by a teacher.
A sketch that interprets remote control input and operates wheels accordingly is one thing. A sketch that somehow intelligently wanders about, avoiding obstacles, taking samples, returning to base is quite another.
At first, start with a sketch that just - I dunno - drives the robot around in a circle for 5 seconds. To get to that point you have to at least get an arduino talking to your machine.
In parallel with that, work on a sketch to get your arduino talking to a zigbee. At the very least, you have to think about how you will be sending the commands. A hand-held remote control with another arduino and zigbee? Ok, fine. you'll need a pair of arduinos with the comms gear, and you'll need to work out how to get them talking.
With that done, it's time to think about what you want them to be saying. Easiest way is probably single packets, each one a C struct. The robot is sending whether it's hopper is full, maybe sending its gps location? The remote sends - well, I dunno. IN the simple case, steering wheel, stop/go, take sample.
More complex, send GPS coordinate to navigate to. Robot has a bump sensor and a maze-running algorithm. Sender will need some way to enter GPS coodinates: keypad and LCD screen? Get rid of the arduino remote and just use a PC?
Your first problem is working out what you want.