Today is the 1 year anniversary of leaving my idiot drunk ex (german) and father of my 2 kids (6 and 4) here in Germany (BW OP if you are in region, PM me :) ) I haven't lived in UK since 2007, and had/have no intention to live there again. Kids were born in a third european country. we weren't married so it SLIGHTLY alters the situation for me here in Germany, but yes, without his written explicit consent you can't leave with the kids (I took some advice before i left, though not with a lawyer)
I was a SAHM when i moved out, but the jobcentre were really great and helpful and non judgemental, and i recieved very generous benefits as a single parent, plus they paid the rent in my new apartment and i went on a language course for free for 4 months (i spoke german but not brilliant). Now i am self employed as a cleaner, not with the jobcebtre anymore and doing fine. He will have to pay maintenance, to kids, and you as you were married (PP mentioned Düsseldorfer Tabelle) and it will be taken direct from his pay if he tries not to pay it. Kindergeld is good, job opportunities are good here, medical, school, kindy, it is all better.
I will stay here for next 15 years until kids finish school and then I will go back to the third country again. I don't have loads of friends or support here (EX is pretty useless) but its ok and I really think better than you would get in UK and anyway, ultimately you may have no choice.
But now, of course, you are in shock and it took me a couple of months to get my head round the idea i would stay here, but now, I am even considering buying a house next year, if i can!
Something to consider is, if you stay in Germany and want to move to a new village/town, you can only move up to 200km from the other parent under German law, so you couldn't hot foot it to the other end of the country to escape him. But you certainly could move to a bigger town with much more possibilites for you.
In my local town there is a Verein for Alleinerziehendeeltern and they gave me free advice and had a meeting once a month for single parents to meet for friendship and help etc, they also, if you joined the verein, offered free lawyer appointments. They may have one in your local town, google and see.