Hi L.,
The Rosin Eyecare Center at Loyola Medical Center (on 1st Ave. in Maywood) has just the glasses you're looking for. My two-year-old has been wearing them since she was 6 months old. They're made of a bendy plastic that won't break, and if the kid really twists them hard, the lenses pop out instead of cracking. They're inexpensive compared to regular frames too. I don't remember the brand name, but manager Erin Brennan will know exactly what you need.
The number is ###-###-#### and it's located on the first floor of the outpatient center at LUMC.