I've had many a problem with grass loving ponies. What i find best is when they do put their heads down instead of giving hard long tugs on the reins wiggle the bit and do short tugs quickly and keep doing that until the pony puts his head back up and he will as long as they are sharp and sweet as the pony will find this uncomfortable and will find it harder to eat the grass. Also as your daughter is trotting or whatever round, slowly wiggle the bit to remind the pony that she is in charge and that he must listen to her. While she is still nervous a lead rein might help so you can help stop her falling off and reasure her. Hope you get the problem sorted as it does just sound like a heirachy issue in which your pony is just taking advantage.