Where on a child's passport does it say what nationality the mother is ?

It DOES state that he is a BRITISH citizen, so providing his visas/balikbayan stamp (if required at that age) are in order and therefore he is not an overstayer, what authority do the Philippines Immigration have to stop him from travelling ?

I also have two Filipino step-children.

Now the question of THEM leaving the Phils (Filipino passports) when still minors was quite a different matter.