Toy with Badly Cracked main PCB
Unfortunately, the multiply fractured main circuit board shown in your picture is not repairable by less than extreme methods.  It's a cheap paper-phenolic board notorious for cracking when stressed, but can be cranked out in a factory for pennies.
You'd need to source a replacement, and such are not usually sold for mass market toys, especially not those of western banding and where the board is buried deep in side.  (One slight exception is that spare boards are available for some cheap drones; but there the board is exposed, and much more likely to suffer crash damage - and even then, only a minority of brands sell them).  Even in the unlikely event they were sold, questions about finding where to buy things are off topic on this site.
If this were an item of orders of magnitude higher value than it is, a skilled technician could probably attempt to glue the board back together then repair enough of the broken traces to get those sensor/actuator wires re-integrated into the circuit.  Or to re-assemble it enough to take a picture and then transfer the components to the new board designed from that.  But that's hundreds to thousands of dollars of labor equivalent unjustified for a simple toy, unless you have the skill to do it yourself and the emotional attachment to an irreplaceable treasure warrants it.
An interesting alternative would be to try to replace the board with something custom; if the child is reaching an age where programming projects become plausible, a &quot;brain transplant&quot; based on some experimenter MCU platform (Arduino, circuit python, Espruino, whatever) could be quite rewarding - but would take a lot of work to figure out the sensor/actuator interface.
Or maybe you can find another of the toy broken in a different way, and get the board from that.