I think you're already figuring out that teaching ESL is not a long-term career plan in the U.S. unless you teach children in the public school system.
I'm just going to rant here a minute for anyone reading this who might be thinking "Hey, ESL teaching sounds like a fun job!" When teaching adults in the U.S., almost all jobs are part-time, with no or very few benefits. The pay is about $12-$20/hour, whether or not you have a master's degree. Classes go for a few months and stop. You will not get paid during these breaks. It is unlikely that you will get sick time or paid time off. You might even be paid as an independent contractor, meaning that you won't even have taxes paid by your employer.
Most jobs are at for-profit schools (that charge international students a hefty fee for classes, of which the instructor sees little). Many do not pay for prep time, only teaching time.
You will get paid the same whether you are fresh out of school or have been a teacher for 20 years. Wages have not risen in years. Nonprofits, where low-wage immigrants students take classes for free or low cost, are nicer places to work, but pay the same or less as the for-profits.
You will be lumping together multiple PT jobs, in different parts of town, to make a paltry annual salary. You will have very little say in when and where you teach, or how you teach in many cases. The OP mentioned the erratic schedule. One school will have classes, say, from 10 am to 1 pm, 3 to 5 days a week, and another will have them from 9 to 12, making it impossible to work at both places. Or you will be working from say 9-12 and then from 4 to 9pm on Mon-Thurs, and then 12-4 on Saturday and Sunday -- not ideal for most people.
You will NOT be working 8 hour days from 9-5, 40 hours a week. You might be lucky to get 20 or 25 hours. And that is all classroom teaching, which is extremely energy-intensive -- I am not sure anyone could take active classroom teaching for 40 hours a week anyway. Did I mention that you won't get paid for prep time, or if you do it will be for maybe 1 or 2 hours a week?
TESOL certification usually costs a couple of thousand dollars, or more. It will take you months of PT work at $15/hour to get that back.
Adult ESL teaching certainly isn't a career compatible with supporting a family, and is barely adequate to support yourself. Again, overseas this may be different, but in the U.S. -- forget it. I consider adult ESL teaching to be rather a scam, on many levels, and a situation akin to adjunct English teaching in colleges. The students pay a fortune, the teachers make next to nothing, and the "school" (that is, the company) gets all the money.
Back to actually addressing the OP. I don't know enough about differences with a master's degree re getting jobs, but if you can somehow get into non-adjunct college teaching, say at a community college, that might work (though the "real" professor jobs will require a PhD in linguistics or rhetoric or something like that). Getting certified to teach in the public schools might be your best bet, assuming that you like kids -- and you don't need a master's for that.