If you've got the mind, you've got true control, but as far as aids go, it's the whole corridor of aids: seat, legs, then one rein last. Two reins makes an out-of-control horse more claustrophic & apt to run off due to the pain.
This I disagree with.
Two reins is a reinforcement que, not a snatch and yank and pull cue. If a horse is in pain from being touched with the reins, it won't matter if it is one rein or two. If the horse is claustaphobic, it will run away from the one rein pressure because you have managed to "open the door" to the rein you aren't using. Seen a lot of colts improperly taught to do a one rein stop who will run sideways like that.
On top of this you have zero hope of ever
getting a straight stop if you only use one rein the entire time. You will get a horse who bends, blows their hip out, and sure you might get a stop but there's no balance, no finesse, and no hind end drive which the OP will absolutely need if she is going to do drill team. You can't have a horse just flopping into a one rein stop, and if you can't get a horse stopped with two reins (Actually, no reins for that matter) there is a hole in your training that you need to address.
If you pull back on both reins and this horse runs off like a rocket, head in the air, bracing, bolting mach 20...Yes, get a one rein stop and kick his hip. I mean really kick his hip. Make him bend and move, because that is a complete lack of respect and he needs to think twice about doing that again. Remember when he relaxes to always release the pressure and pat him, praise him, etc. Right thing easy, wrong thing real hard.
However, do not do to the one rein stop unless you have to, and if you know you have a dangerous bolter do NOT start off at the canter or even at the trot. Get a loose rein, STRAIGHT stop at the walk first. Then the trot. THEN the canter. By that stage you shouldn't have a horse who even thinks about running off if you have prepared him, and the second you feel even the slight inclination to a fractional increase in speed...Back him off your hands, stick his butt in the ground, and back him up. Rollback the other direction and go the other way. Take away the forward motion and make him do something else.