Joe writes:

I'm going to use Gorilla Glue to join the pieces because
it will expand into the holes

You have no chance of succeeding without analysis of the species of plastic
and what will bond to it. Few plastics admit a glue bond anything close to
the strength of the original material (which, after all, itself failed), so
your quest is quite futile. The notion of pinning is misconceived.

Polyurethane glue such as the overhyped brand you mention has its
applications, but this isn't one of them, and you shouldn't be suckered by
the phony labeling into thinking it is.

Glues and stuff to pour into your car are sold as easy miracles to solve
hopeless problems. It's best to learn that not every claim on the retail
shelf is credible, despite your natural credulity. Save your child's wonder
for the toy store, and develop your aging cynicism for $10 bottles of
stickum.