The sentence you wrote is almost correct, but it can be made simpler and clearer for a 4-year-old. Here's a corrected and easy-to-understand version:
"The brain has two halves: the left side and the right side. Each side controls the opposite side of your body."
This means the left half of your brain helps move and feel things on the right side of your body, and the right half helps with the left side of your body.