What is the best/most economical digital camera to take professional looking childrens photos?
Professional photographers take professional looking images, cameras do not. You could buy a Nikon D3 or a Canon D1s Mark III and still get garbage pictures becasue you (a) don’t know how to use the gear and (b) have not mastered the basics of photography. I would spend the money on education and stick with the camera you have now. Once you are ready to upgrade, you will know what gear is best for your needs.