Sorry but "get stronger and beat him" is absolutely not what needs to happen, and it's a bit of a concern that you think that's what you should be aiming for here. It isn't about "beating" or "winning". The horse is a youngster. He's LEARNING. Young horses need a rider with the skills to teach them what to do and how to do it correctly.
From what you've said I absolutely do not believe that this horse is right for your daughter. But since you've made it clear you plan to continue, my advice would be to make sure the horse is being educated on a regular basis (like, several times a week) by an experienced rider who has the skill and confidence to produce a youngster correctly, and that your daughter only rides under the supervision of a competent riding instructor so that she can work towards reinforcing what the other rider is teaching him.
I don't know if you've heard this, but horsey people have this phrase, "green on green = black and blue". Let the current situation continue and your daughter could, at best, lose her confidence, and at worst, get hurt.
Not only that, but the horse is going to learn bad habits and go forward with massive gaps in his education.