My feet slip a little too. I have found a brand of socks at Target that are comparable (IMO) to the Thorlo socks, they are called gold toe. Women's gold toe with arch support (they're thicker and tighter around the instep) and the elastic is just right. They come in low (short, crew style) and higher (so you fold them over). They really last through many washings... Anyway they help with that slippage problem. I was feeling that just the other day during the Boot Camp sumo squats.
Some moves really test your shoes, though. I find that my feet slip a little but it's controllable. I use KSwiss (whatever the model number--they change every so often) with a smoother sole. Every foot is different, but these tend to fit my feet well, and the sole allows most comfortable pivots on carpet. Also doesn't trap rocks and mud if I ever venture out-of-doors with them (I do that with last year's models!) Actually I can go more than a year per pair.
The lateral support on these is quite substantial. They seem to hold up well with use, and they are light weight. The price is relatively good at under 70 dollars a pair. I found them at Foot Locker or Lady Foot Locker.
But Leslie, I doubt you are at risk for an injury unless your shoes slip all the way around, LOL! Remember that the way you land makes a little difference. Working the small stabilizer muscles around the ankle by doing these moves in a controlled manner helps prevent susceptibility to ankle sprains and strains (turning the ankle).
-Connie