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 :)
"Strength is the ability to use a muscle without tension"