13a Visa for Chinese national

I am really not certain what privileges (or otherwise) Chinese citizens have in the Philippines.  You should already have sorted out the details of that aspect at the Philippines Embassy in China. But as regards the fact that you are married to a Filipina, you would normally be eligible for a Balikbayan visa on arrival which is valid for 1 year. I am assuming that your wife is still a Philippines citizen at this time - which is why I am just a little puzzled why you applied for a tourist visa in the first instance - perhaps your son being a Chinese citizen complicated matters?  As I said above, I am not certain how Chinese nationals relate to the Philippines immigration laws so this might have had something to do with the pathway you chose. In regards to applying for a 13A, which would allow you to stay in the Philippines indefinitely, I have a feeling that you should be in the Philippines during the application period just in case you are called by the BOI. I am not a Chinese citizen myself, but I was advised that it would have been easier for me to apply for my 13A at the Philippines Embassy in my own country. I think in the Philippines it can take a number of months for processing. Initially you will be given an interim 13A which will become permanent at the end of the first year.
I am wondering if you visited your nearest Philippines embassy in China. Or did you get your tourist visas from the travel agency? In any case I would well advise you both to go to the nearest embassy and find out what is your best way to proceed. If you come to the Philippines to apply you may be asked to provide some documents that you can only access in China
I have a feeling that, unless everything goes extremely smoothly when applying for the 13 A in the Philippines, 60 days may not be sufficient - again I would advise you to visit the Philippines embassy in China.

Best regards Bill