You need to look into the action framework. 

Your button needs to be of type “Run Multiple Actions” 
Then one of those actions needs to be “Update field on row”  – where you choose a model build on the child object and update particular rows.  

Note:  your button will need to be on a skuid component that is in the context of the Parent model.  IF it is on a page title component - make sure the model context is set to the parent object.  IF it is a row action on a table,  you should be good. 

If you are comfortable with the booleans always being in synch - this will work.   If your requirements specify that If Parent = False child CAN = True you will have to create a more complicated If - Then statement,  which would need to happen in a custom snippet. 

Cheers.