I think the top two options are:
- Avoid taking photos when the sun is harsh; wait for a different time of day or for cloud cover.
- Make use of the geometry and patterns of harsh shadows for interesting composition.
Neither of those actually answer your question, though. Presumably, since this is playground photography for a moms' group, you're taking pictures of small fast-moving people, so HDR techniques where you combine multiple images are out. Failing that, taking your images in RAW will let you stretch the dynamic range in post-processing. (Use your RAW converter's tools to bring up shadows and bring down highlights.)
Also, experiment a little bit with your camera and see if you get better results with the camera's metered exposure or by exposing a little brighter and bringing it down in post-processing or by exposing darker and bringing up. The first will give better detail and less noise in the shadows, but highlights (and a possible overexposed sky) will be worse; the second will give more room in the highlights but make the shadows worse.
If you aren't shooting in RAW, your camera may have features for increasing the dynamic range in the output. First, find the contrast setting and turn it down a few notches — the scene has plenty, and this will increase the dynamic range. Second, look for features like "adaptive lighting" or "highlight control" — these will do basically the same things you might do to a RAW image, although with less control in your hands.
These things will help a little bit. But, really, I'm going to go back to the first suggestions. On bright days, stick to close-ups where you can either control the light or at least reduce what's in the frame (so you're shooting only in the shade, or, better than nothing, just a well-lit area). Get out your longer-focal-length portrait lens and get in close. Or wait for shots where the shadows are interesting themselves. Then, take the wider shots on cloudy days.