Many of our clients struggle to do push-ups simply because they cannot keep their body in the proper push-up position. And how can you do a push up if you can't keep your body in the proper position? Simple answer, you can't. The one exercise that we use to develop this ability is the straight arm plank.
We have our clients begin this exercise by starting on their hands in knees (hands directly below their shoulders and arms straight). Then we have them raise up onto their toes and slowly walk their feet back until their back is in a straight line. The number of times that they perform the exercise and the amount of time that they hold the position varies based on their comfort and ability level.
Try doing a few sets of these with your child and let us know how it goes!