how to enable (Also Publish/Unpublish in Child Publications) option automatically checked using Tridion 2013 SP1 -HR1
There is no out of box feature which will help enable automatic selection of the checkbox. You will have to write a GUI extension for the same which is the right way to go about it for implementing this kind of functionality. For details on how to write a GUI extension, you can refer the following links:
As Vipin says, you can write a GUI extension to do this, but with this kind of thing, requirements are everything. What do you want to achieve? If it's simply about checking the checkbox, then use a GUI extension. If you want to change the semantics of publishing so that child publications are always published, then you can enforce this by writing an event handler. In that case, you may still wish to write a GUI extension so that you don't have a misleading checkbox.