The simplest way to power the rover and power the PICAXE is to use two different power supplies that share a common ground. To power the PICAXE, you can use the Snap Circuits B5 block (it is also called a 9 volt Holder and Switch). The advantage to using this block is you can connect a standard 9 volt battery to the block and it will deliver a reliable 5 volts to the PICAXE through L7805 voltage regulator circuit (see circuit schematic). The B5 also has two 5 volt outputs--one to power the PICAXE and one that you can use to power another device.
Now you have a convenient way of powering your PICAXE with a reliable 5 volts from the B5 block. As a safety feature for the PICAXE, it would also be a good idea to keep the 9 volts from the rover separate from the PICAXE in case while you are building and testing the circuit something gets connected the wrong way. Thus for this build you will use an H-bridge. It has special circuitry inside it that will prevent the 9 volts from the rover's battery pack from accidentally passing through the PICAXE.
Picture source: www.snapcircuits.net/downloads/ic_info.pdf