BTW - She already called a local aerial company who wanted 300 quid to move it (and presumably 300 quid to move it back again when all done)
They're having a laugh. Putting up a dish isn't that difficult. The hardest thing really is mounting the bracket / pole, as the wall fixings are quite sturdy.
Yes you can move the dish with the cable still attached if the cable is long enough, but I wouldn't stress over that too much, as it's not difficult to disconnect.
Before doing anything, turn the Sky box off at the wall, as the box sends power to the dish and if you short the wires you can damage the box. Also note which way your dish is facing (roughly SSE) and the elevation (vertical tilt).
If you look at the LNB (the box on the end of the dish 'arm') you should see the cable connecting to the underside of it. The connector is usually wrapped in amalgamating tape, so you would need to slice through this with a knife. Once the tape is removed, the F-connector simply unscrews. Note carefully how to re-assemble the connector. It's important that the outer braid doesn't touch the centre core when you reconnect the dish. Chances are the cable is tie wrapped to the arm, so cut through these too. Your dish is now free!
Move the wall mounting / pole, keeping in mind that the dish needs to be at least 8 feet above ground. Make sure the mount is vertical (they often have a spirit level). Re-alignment of the dish can be done as previously suggested with a meter from Maplin, or visually by moving the dish till the picture appears.
As a silly suggestion, why not leave the cable connected, detach the dish from the wall, wrap it in a black plastic bag and dump it on the ground until your building work is done?