I also have a special needs child who has low core strength. I know you are asking specifically about trampolines and we have a small one in our house that he can use indoors. It has a handle on it for safety. However, our physical therapist has given us a number of exercises and fun ideas to help strengthen his core. Currently, he swims twice a week which helps greatly. Daily, he uses an exercise ball and does a number of different exercises with it that are specifically designed to build core muscles ie. situps, picking up the ball and bouncing it to me, etc. We also have a home made balance beam we use to aid him with this. Wii Fit is another tool we use and it has helped him with balance issues. I think the trampoline can be a great tool but I would be concerned with a larger one. Our PT suggested a small one with a bar because she said kids with low tone are more likely to become injured and me being the worry wart that I am I could not bring myself to buy a bigger one.