First of all: good for you! Finishing your degree and getting your qualifications was an amazing achievement. I hope you are patting yourself on the back.
So I'm surmising that AH did a 180 somewhere in the past six months? Today was the first I read your thread. While reading your first posts I did have a sneaking suspicion that he would recant when he realized that leaving you would mean no more comfy home, no more security of having a partner.
I'm really sorry that the man you fell in love with morphed into a jerk. Maybe it was all the years of alcohol abuse, who knows? It's not your fault.
Now I'm going to echo Kilt and say attorney attorney attorney. You seem to have decided on your own that his threat to take the kids has merit. And since you believe his threat you've decided to give it another go, not out of your own desire but because you don't want to lose the kids? You're making some huge decisions based on guesswork and fear.
So see an attorney. It doesn't mean you're starting a big lawsuit, it means you're getting information. If you're on low income, you can get a consult for free or cheap. Find out what your options are.
I can say as a paralegal that I am *so happy* when someone comes in for advice just when a problem is beginning, because with the right advice and knowledge from the get-go, most problems easily solved. What makes me bang my head on my desk is when someone comes in *after* they've got themselves in a big mess. I'm like, "But this could have been easily avoided, why didn't you get legal advice sooner?" and they're like, "Well, my friend told me...I read on the internet... I thought a lawyer cost thousands and thousands..." GAH.