Lytro -- photos of toddlers/kids
I have a Lytro camera but no toddlers; I'd say a definite "maybe."
The camera has two modes. The easiest is the Everyday mode which allows everything from about 4 inches to infinity (about 6 feet and beyond) to be refocused. The problem is the camera has a narrow field of view so if the kids are running around you'd have to shoot a bunch of grab shots and toss most of them. If the child is seated, then I think you'd be able to get some nice pictures. But then, if the child is seated, you'd probably get better images with a $100 camera or your phone.
I really like my Lytro, but it's certainly not "idiot proof," as some superficial reviewers claim. It's a demanding camera but can take magical pictures with experience and luck. I suspect that you've got your hands full with your child and the Lytro would require more time and effort than you currently have free. IMHO.
This is the first image I took when I got my camera; it's a grab shot of my puppy: