Spanish & Filipina Marriage with a kid. Transit in China

Your itinerary is definitely eligible for 24 hour visa free transit and you do not need any kind of visa. To be precise, you and your son do not need anything because Spanish citizens can enter China absolutely visa free in the same way as you can enter UK. It is your wife that will have to apply for a temporary entry permit at transit counter immediately upon landing in Beijing. This is not a problem at all. So, before your landing in Beijing you will get an arrival/departure card for China on board the plane. You will fill out all three arrival/departure cards and upon landing (you will tick the box transit in the card), you will all approach the transit counter. Your wife will apply for a temporary entry permit by presenting flight tickets as well as hotel booking confirmation. After a short check, she will be granted a temporary entry permit and you will all cross the immigration in order to have a good night rest in the hotel. This application is free of any charge.

This is a very simple situation and you do not have to preoccupy yourselves with the situation because you are fine to go :)