ILA vs Apollo - CELTA course worth it in Saigon?

Yes, what you heard about the CELTA is correct. There are some schools that only hire teeachers who have one.

On the other hand, as a woman and native speaker of English (right?) living in Sài Gòn, you should have no difficulty finding teaching work, most of which involves teaching kids.

So, getting a CELTA will mostly depend on whether you intend to make a career out of teaching in various countries.

Another factor is that you have your child to take care of and the CELTA as you noted is a challenging full-time commitment lasting a month, I believe. So, doing it later might be a better choice.

Finally, with regard to work, this time of year leading up to Tết is when schools have the least demand for teachers, so initially you may not get a lot of response. Anyway, do a search for "Vietnam teaching jobs" and you can see some job ads to get some idea about requirements, duties, pay, etc.