Lounge Longe Lounge! Lol Lounging allways helps.
Get him to respect you (or in this case your daughter) on the ground first by getting him to focus on her. Move his hip back him up and so on. And allways make sure that he respects her space. Have her streach her arm infront of her and he should be that far away. That just means he respects her space and he's out of 'the bubble'.
After the groundwork, and your ready for undersaddle work, make him give to bit pressure at the halt, walk, trot, then canter. Just pick up on the reins and hold it there till he tucks his head in (gives) the immeidiatly release. Do this alot till he gets that when she picks up on those reins he is to give to her. Then do it at the walk, trot, canter, and so on. That will make it easier to control him. Make sure he is lounged and he does these excersises every time she rides untill he gets easier to handle.
My filly had the same problem but she's improved alot since I've done that. When he pulls his head down like that it's becuase he is trying to avoid the bit contact and also makes it easier for him to buck.
Also if he gets a little faster than he should or bolts and she can't stop him, then turn him in a circle or pull his nose around the side.
Hope this helps! :)