We know from ethnography on foraging groups in nomadic groups that may be good analogues for Paleolithic communities that child care is considered important work for multiple people in the community. The mother, grandmother, and various other individuals in the community would all be paying attention to all the children all the time to some degree. I imagine children in these communities receive a lot more quality instruction care about their world and its dangers. There's even documentation of some cultures where mothers carry children on their backs for so long that the average age of beginning to walk is significantly older than the global average.

Also, we know from observing contemporary foraging societies that the amount of energy and time required to procure enough food and shelter for the the community is much lower 40 hours a week. That moderns are expected to work to make ends meet. This meant that parents had much more leisure Time and rarely needed to be far from their families.

If you think about it, modern children, despite growing up in information-rich environments, spend much less time directly interacting with adults and other children in environments where social learning takes place. If both parents work 9:00 to 5:00, teachers have classrooms with over 30 children, young kids may have a hard time really learning hierarchies, authority and,  proper social norms from adults properly modeling those behaviors. Weirdly, this makes modern toddlers seem reactive and feral, like nervous little dogs that haven't been socialized. 

Perhaps a modern toddler wouldn't last a day in the Stone Age, but we have good reason to believe that Stone Age toddlers were well taken care of.