Wow he sounds absolutely vile, won't even give you any until your benefits have gone through! What a joke.
I was in this situation this time last year, it was vile, I know how you feel. My ex did give me money until my benefits were sorted but I couldn't afford the rent and just barely afforded the food shopping. I felt so depressed, didn't eat, and drank loads of cups of tea instead. I'd put dd infront of the tv and sit and cry in the kitchen. It has to be one of the shittest times of my life. I wanted him to come back but he refused.
Although it is so shit right now and nothing anyone can say will make you better, all I can say is things WILL get better. It won't be overnight and you'll feel like shit for a bit. Once your benefits are sorted things should get easier, take the kids out to the park or anything just get out of the house, fuck your ex you will meet someone better in time. Enjoy your kids and smile because there is so much to smile about!
Always have something to focus on, put the music on loud and declutter the house, decorate the bathroom, play hide and seek with the kids. Anything to get your mind of the situation.
I hated having no money and my ex loved the fact I was reliant on him, the beginning of this year I got myself a cheap laptop and webcam on my credit card (Don't bother judging me) and I started web camming on adultwork when dd would be in bed, I sit there in my bra typing and I earn more than enough money, I've took dd abroad twice this year, it has honestly saved me. I don't claim benefits anymore. If you can I'd give it a try, I don't know what I'd even want to do now career wise. A lot will judge my comment but I have been in this situation and it helped me out great deal.
Good luck and remember this horrifically shit time won't last forever!