The horse is not responding to your daughter in all ways? I mean won't go, won't slow , won't turn, leads poorly or other ground manner issues?
I ask because if he responds poorly all around, it is in his head. He does't see her as having the authority to be a leader to him. So , he can "blow her off".
It is certainly wise, IMO, to use a gentler bit until your daughter has the hands needed to hold the curb bit well. But, this alone will not make you daughter capable of getting the horse to do what she wants.
She may need a bit more assistance with how to get a horse's attention and obedience on the ground, as this will increase her position as leader in the horse'e mind.
As for a bit, I think a simple snaffle, perhaps a D ring, would be best.