Nothing to worry, they have to use the Filipino passport to enter/exit the Philippines (you must ALWAYS use same passport to enter/exit a country) and have an illimited stay duration there. At the exit, showing also the British passport will act as a visa to let them go out. To exit/enter the UK, use the British passport (same ALWAYS use same passport to enter/exit, are both are recorded by Immigration). In case of questions on your stay, just show the Filipino passport will be the Philippines immigration stamps.
Just always have a copy of kid birth certificate and of your marriage certificate in case of questions at immigration (it's not requested but can help sometimes).