rein cues vs. leg cues?

So my daughter (age 9) for a multitude of reasons takes lessons from two differerent trainers. One trainer comes from an eventing background and seems to emphasize using the reins to move the horse, I.e. If she wants my daughter to keep the horse near the rail she will ask her to use her outside rein and she doesn't seem concerned whether her horse is bending in the corners. The other trainer is from a paint/western background and she wants my daughter to use more leg, I.e. She asks her to use her inside to push her over and to bend her in the corners. So my question is, is this personal preference, discipline preference or one trainer is more right than the other?

Honestly you need both. Your hands are important, your legs (and seat) are important.

Since she's beginning, I'm guessing, the eventer probably has trained her horses to follow their nose, aka use the reins to guide them to stay put. Kids' legs are usually not strong so horses don't usually pay mind to them at times.
The other trainer wants to give your daughter a good foundation by using legs and less hand.

Both are right, they're just teaching from different starting points.

There should be a harmony of seat, leg, and hand aids when riding a horse, but that usually is found as they become more advanced since giving seat aids is really confusing when you're still struggling to find balance on a horse, etc.

Hope that helped. I ride English, but have also ridden a little western too :)

Agreed with the above. But I'd let your daughter know it's okay to use both if she ever finds using just one s a problem.