This could be achieved either via a Flow or a Business Rule with a scripted action. While it may have more overhead, I'd recommend going with the flow option, as it will be easier to maintain.

I'd create a Flow that triggers when an incident is created or updated with the condition that child incidents is not empty and that one of the fields you want to copy has changed.

Under the actions, have a Look Up Records action, which gets all incidents with other condition of Parent is Trigger - Incident Record (data pill).

Once you have all the children records from the Look Up action, you can use the For Each logic and add the Update Record action item and set the fields as needed. For more information on how to create and configure Flows, I recommend this course on NowLearning.