Hi everyone, I'm a writer currently living in Wenzhou, China and my husband is an English teacher at a private school -- teaching kids after their regular school days and on weekend. He does have a TEFL certificate but not a Bachelor's degree. Some teachers at his school have a Bachelor's but not a TEFL certificate (I think they struggle more as they don't have the training on how to teach a language).
For China, you absolutely must have the job offer before you come as you need a working visa (good for one year) and they will not give you one from inside the country.
Dave's ESL Cafe is a good resource for finding jobs. Just do your research to ensure you hire on with a good school and in a city that will meet your needs.
The issue of coming with your son does add to the complexity of your situation. We have a woman from Russia teaching at the school and she hopes to bring her son after he finishes his school year. Everyone is learning how to do this as it is a fairly rare occurrence.
If you'd like to discuss more, please e-mail me at doris@dorisgallan.com
Good luck,
Doris