I just want to share a couple of little stories. My old horse Buck was a monster of a horse, standing around 16 hands and weighing around 1400. When my brother was young, maybe 6 or 7, he was leading Buck back to his stall at the show ground. As they were walking, an electric cord brushed Buck's rump and caused him to pop his head up. My brother had a tight enough grip on the lead close enough to Buck's head that he was pulled off his feet. He sprawled out on the ground in front of the still-walking horse. Buck took a step and ended up with his foot on the side of Jason's knee. He didn't move another muscle or try to take another step, he simply dropped his nose down to my Brother and stood there with his foot barely resting on my Brother's knee. He stayed exactly in that position for several seconds until my Dad could get there and show Buck where it was safe to move his foot to avoid the rest of the arms and legs that were underneath him. Even after all that, the only mark to be seen was a hoofprint of dust on my Brother's jeans.
We had a team of Belgian Mules named Buster and Tiny. Both of them were over 17 hands and weighed more than 1500 (though Buster was quite a bit bigger). When they were about 5 years old, we had them at a Mule show. Dad was leading them down the isle of the barn to their stalls when Buster froze and refused to move. When Dad turned to see what the deal was, he heard a squeal and giggle from directly behind the mules. Apparently, (according to other witnesses) a young girl of 3 or 4 had wandered away from her parents and when she saw the mules, she hit a run towards their walking hind feet. She never even slowed down as she hit Buster's back legs and wrapped her arms around them. He never reacted other than to freeze every muscle, lift his head, and cock his ears back.
These are the type of reactions that absolutely cannot be taught, they must be ingrained in a horse's being so deeply that they are simply unable to react badly to a child. The horse from the first story, Buck? If that had been an adult, he would have run them over and sneered as he trampled them and kept going. His lot in life was a kid horse and that was what he was best at. For a kid, he would kill himself doing what they wanted to do so long as they were safe but an adult would be hard pressed to successfully ride him without a big fight.
I guess what I'm trying to say is that some horses don't like children and never will. Regardless of what kind of training or desensitizing Honey gets, she may never be comfortable or safe around kids. Probably your best bet would be to continue on with the way you are doing things now, keep the girl away unless you are right there to protect her.