Agreed with what Mango said. :) You and the horse are both leaning to the inside, and when that happens at high speeds, you'll probably slip and fall...But, in those photos, I don't think you're flying at NFR speed so it was probably no biggie. :) But yes, you need to get the horse lifing its shoulder and its inside leg up under them so they can drive off the turn on their hind end. That will just come with a lot of slow work. Also, weight in your outside stirrup instead of your inside. ^^ When you're in a western saddle you will sit down when you're ready to turn, put your weight in the outside stirrup, hold the horn with your outside hand, and direct rein using one hand pulling to your hip.
All in all it's not bad, for an english rider.
Seriously. Come to the dark side. We're pretty fun over here too. ^^