I have an appy too, but she's quite a bit older than your kids.... she's about 20.
Im sorry to hear about the less than ideal work area, I know how frustrating that can be, though I kinda have to opposite problem, too much space! My appy can't walk a straight line w/out a fence and my parents refuse to fence a work arena!
Anyway.... you are absolutely right to work more on the bond with your horse, especially since she is so young. When we had a foal, our focus was on bonding and trust, that has made the entire training process 100x easier. When it came time to walk onto the big scary trailer all alone with no mommy or gramma, she followed me right on as though she had done it a thousand times. Because she trusted us. So keep up the bonding and just be patient, she is only a baby after all.
Also, since she is only a baby, I would be EXTREMELY slow with the jumping lessons. Even at 4 her bones/joints/muscles are still growing and developing, and jumping is one of the most strenuous tasks we can ask of our horses.