I agree with Knaagdier. I think that the lunge line would be a good place to start with your daughter on his back, but please make sure you have an experienced horse person on the end of the lunge line too so they can attempt to control the situation if it gets out of hand. I wouldn't want to see the lunge line get dropped if he pulls too much and then you will have him loose with the "scary snake" chasing him
Maybe use of a round pen? He might behave in a smaller space and I think he would have a harder time breaking through it.
I think that you can most certainly beginning working on his back. He is 4 and it sounds, from your description of the situation, that you certainly aren't going to be overworking him under saddle anytime soon. With baby steps, ground work and lunge work you will probably still spend a lot of time getting him going. There is always a big debate in he horse world of when to start horses, so I'm not going to get into it here, but I think at 4 you are more than good to go.
Finally, a quick question, what strategies does your daughter (did your trainer) use when he is getting "out of control"? Just a pull back, circle, head to butt?