A couple of principles should guide your purchases of hiking gear for children.
First, the longer and more complex the hike, the more equipment and supplies you’ll need. Since you’re day hiking with kids – meaning you’re just hitting the trail for a couple of hours – you won’t need to splurge on the most expensive equipment or on a lot of it.
Secondly, your general goal is to go light. Since you’re on a day hike, the amount of gear you’ll need is a fraction of what backpackers shown in magazines and catalogs usually carry. Indeed, the inclination of most day hikers is to not carry enough equipment. For the lightness issue, most gear today is made with titanium and siliconized nylon, ensuring it is study and fairly light. While the list of what you need may look long, it won’t weigh much.
Read more about day hiking with children in my Hikes with Tykes guidebooks.