it's normal for a tire to move back and forth the amount you described. everything flexes - frame, wheel, probably the trainer.
did your trainer come with a different skewer? I have a cycleops that came with a skewer that fits in the trainer - it's by far the most stable trainer I've ever had. if it didn't then you should get a big lumpy steel skewer.
I've ridden a TCR carbon mainly indoors for most of the year (I can't ride outside a lot due to work) with no problems. I've ridden aluminum TCR's indoors for years with no ill effects. a short trainer ride is 30-45 min, a long one is 3-4 hours. so I ride on the trainer quite a bit.
I imagine the warning for CF (and prob AL) frames are for those trainers which clamp the bottom bracket or other parts of the frame (fork, seatstay, etc). some of those fork mount trainers really put a lot of force on the headsetarea since the fork is locked in place and cannot flex naturally fore and aft. I've ruined a couple headsets on fork-clamp type trainers. and knowing the litigous US, people will sue after they mar/crunch their frames on trainers. of course I'm no manufacturer so I don't know for sure.
cdr