Make sure that YOU as the rider are NOT looking at the barrel. You want your horse to go where you are looking, and you don't want the horse to run over the top of the barrel, right? So make sure you are looking at a point on the ground about 4 feet from the barrel, all the way around. And then aim to get your horse to that spot on the ground.
When you are 1/2 to 3/4 of the way through your turn (depends on the horse), you want to be looking UP and FOWARD to your next barrel so you can make a perfect straight line to it.
Additional slow work exercises you can do to help make your horse WAIT for your cue to turn is to go waaaaaay past the barrel in slow work. Or simply don't turn it at all. Or turn your horse away from the barrel in a counter bend, before you turn it. All these things keep your horse waiting on you for the cue to turn.
∞•*˚ Βгįťţαňγ ˚*•∞
It is not enough to know how to ride; one must know how to fall.