So I help train horses, green horses, and bring them up. I was taught to either do the things below, and or go in the corner at the trot, while you're trotting around the arena and squeeze the inside leg and "open" the inside, but don't drop yourself! And come out of the corner like that.
Try squeezing with your outside leg in front of the girth and your inside leg at the girth and kiss. The leg position will help your horse pick up the correct lead. Also if your in a arena pick it up in a corner.
If your in an arena try trotting up to the corner and bring your inside reign back a bit and then kick with your outside leg!