David,
I think there are a few ways to get from airport to CdA.
I have driven both the routes below and also stayed on the AP7 longer and exited closer to Mazzarron.
All in all the difference between all the routes is maybe 5-10 minutes.
I would say it depends on whether you prefer to stay on the motorways or use the smaller roads. Also I know some people like to stay on major roads if its getting dark unless they know the route.
The route Gregory suggested is one I have used often enough and from talking to others is considered the quickest. But your route would not be much slower (have done it myself) and keeps you on motorways the whole way which can make the drive easier if you've come in on an evening flight after a longish day
Think the MU602 is now RM2 and then you'd take the RM23 off that to CdA (joins the RM3/MU603 before Campasol). Think the MU603/RM3 runs from "Mazzarron" to Totana.
Shane