Is it possible to remove a coaster brake from a preschooler's bike?
Short answer - no, not easily.

Kids don't have the hand strength to use handbrakes properly, so a coaster brake is going to function better, once he gets the hang of it.  

He's activating the brake by pedalling backwards.  So don't do that.  Instead encourage him to push off with pedals level instead of optimal angle.  That will discourage the rear brake from kicking in.

If you do want to remove it, you're better off finding another rear wheel that fits and lacks the coaster hub.  The local recycling shop here has plenty of bikes for $10, great parts donors.

Can Mister Four ride a 2 wheeler or is he on training wheels?  Has he had time on a balance bike?  He might benefit from "scootering about" on a two wheeler with no pedals first.