I think the state assumes that you get X amount of support and anything over that (they take from him) would go back to reimbursing the state for subsidizing his support $.
You might have to take less money via the state to guarantee SOMETHING, rather than depend on him to step up of his own free will and give you more. It seems a little risky to depend on his sense of fatherhood and right/wrong to support his family. Nothing would stop him from giving you a little extra cashvin addition to what the state takes from him.
I know you are already taking steps to do this, but you need to figure out a way to support yourself and your girls. Don't beat yourself up that everything doesn't happen immediately, even though times are tough, look at the light at the end of the tunnel.