Sunglasses are an absolute must at high altitudes if walking through open areas exposed to the sun and during winter when children can suffer from snow blindness. Look for 100% UV-protective shades, which provide the best screen.
The variety of sunglasses available out there are enormous, but when children are involved, always opt for something sturdy. You can buy sunglasses with no hinges, which means toddlers have one less avenue for breaking them. You even can buy symmetrical sunglasses that can be worn either right-side-up or upside down (for some reason, toddlers like to wear sunglasses upside down). These latter options also cost more money than an inexpensive pair you can buy for kids at any discount store.
Also, be prepared for children to lose their sunglasses. The younger the child, the more likely that the sunglasses will come off sometime during the hike. A lanyard can help prevent this but isn;t foolproof unless you clip it the child's clothing.
Read more about day hiking with children in my guidebook Hikes with Tykes.