I left my abusive ex. Or rather I kicked him out. I accept that I am in a different, more secure position in that it was my house we were all living in.
But I want to talk to you about that fear you've got: I had it too. In buckets. Fear that the dc would be desperately unhappy without their dad there. Fear that I was a failure for letting it all go(funny how even a 'good' marriage -my parents'-can make you feel a failure too!).
Fear of loss, fear of coping on my own, fear of the unfamiliar. You name it.
I suppose the one thing that gave me steel in my veins was the effect him being there was having on the children. He belittled me, belittled them, did as he pleased and was v abusive in ways I only appreciated when I had booted him out. I am a very intelligent, articulate woman, good few years on MN, you think I'd have learned 
Well, you know what, I had a couple of wobbles, but that fear that is so crippling?? It evaporated almost overnight as the rose coloured specs crashed to the floor.
Peace is the word in our house now. Peace.
The dc still miss their father (in his victim bubble and will not sort out seeing them), but I speak to them about it in age appropriate ways and, more importantly, they know they can talk to me about it all, and they do.
That's all you can do. Keep going, keep the tin hat firmly on your head, and get on with the day to day minutiae of parenting. If he steps up and is still a father when you part, then all good. If he doesn't, you and your dc will survive. Kids are amazing.
Go and see a solicitor. It's amazing how powerful a little knowledge makes you feel.