Gday stuartj, both places are known to be pretty good, in fact we had about 20 rellies stay at Free Spirit for out wedding a few years back and all enjoyed it.
There is also the Malak Caravan Park on McMillans Rd, Shady Glen on the Stuart Hwy at Winnellie, and Lee Point Caravan Park on Lee Point Rd. This one is just a little bit out of the suburbs (5 mins) and can definitely cater for big rigs, quite often 5th wheeler are seen coming from there, whereas I'm not certain how the other parks cater for these.
There's nothing in Palmerston, but there's one at Coolalinga, about half hour out of town. Don't know what its like though.
Hope this helps, definitely book though if you know the dates you'll be up, just to be safe. And let us know when you're up for a cold one or three!