What a great update!
You're such a strong woman and you should be so proud of yourself for picking up and leaving.
I'm sure things will continue to get better and better
As for a job search, basically you just keep applying and applying until someone gives you a chance. With everything being online it is hard to make a good first impression and get the spot over someone else because you are good at interviews. I know a handful of people that found craigslist as a good way of finding a job.
Keep moving forward and focusing on you and your children