Get wider at the gates, your actually get fairly wide its just too early and drifting back in. Start behind the boat hips more forward and weight biased on the front foot. Try to keep the handle lower from start to finish of the pull out into the glide and keep your hips up with the front foot bias and come up into the glide stacked. Its hard to get stacked if you don't start out that way. Your a LFF like me, the turn into the gates is like an offside turn so you want to engage the front of the ski more. Check out some LFF skiers on youtube. Chris Parrish, Seth Stisher, Samantha Dumala come to mind. Nick Adams but he does kind of a hybrid one hand gate.
After that its like you say your back on the ski. It keep the ski from coming around so your getting long exaggerated turns. Try to get more balanced on the ski. Sometimes when I start getting on the tail into the turns its because the tip of the ski is getting too sensitive. In that case you need make some adjustments so the ski comes around like you want it too.