Can I go with my husband and son?

I would say that of course someone can go with their family; however, any Tefl program is much more demanding than anyone anticipates. I taught for 12 years and earned a Master's degree in Spanish before doing Tefl and thought that Tefl would be a piece of cake in comparison. The thing is that it is a very intensive one month program and for serious students who want to make the most of the experience and get the most out of their investment it will take up almost all of their time, 24/7. I did go away for one of the weekends but that was not the most relaxing time to visit with my family. So I would encourage family to come before or after.
If you plan on making a permanent move, paperwork is a big factor that is not easy to come by at all.

If the question is about the actual moving abroad and living overseas with family (not just the 4 week TEFL class), here's an article to assist you:

Is it possible to teach English abroad with children?https://www.internationalteflacademy.com/faq/bid/104387/is-…