It is the nature of shaped skis to move along their length and not skid along the width like old style, or dull skis. What you are expieriencing is the ski moving forward and out from under you. This leaves you in the back seat, or your weight too far back on the ski. Flexing your ankle forward and keeping light contact with the tongue of the boot will help you keep up with the skis. A tall, but slightly flex stance is what you are looking for, but not letting the skis move from under you takes a very active role on your part, espicially from the fall line toward the transition into the next turn.
A far as your skis spreading as you describe, have the boots checked for lateral canting. The cuffs can be adjusted for a certain amout lower leg allainment issues and the soles of the boot can be planed to flatten your stance (this cost a few bucks), but the cuff canting adjustment is usually part of fitting the boot.