Chickens generally lay throughout the day. This was a surprise to me, being new to chickens last year, because I had imagined hens would be up bright and early and feeling productive first thing in the morning. But when we're home all day on weekends, we might collect one by 10 AM, one more by 2PM and maybe another one by 4 PM (we have four hens).
Our girls' eggs don't get collected until after 4 PM on weekdays, and there's never been a problem with damage or egg-eating (thank Goodness).
I think your kids would get a big kick out of it.