Congratulations about the new job Lucy. At least from now on you have control of your finances, and can't be sucked dry by EXAH. If he does get a job, he will need to pay child support, but please do what you can to divorce all your financial affairs and obligations from him so you are no longer liable for anything he does.
Is there a financial service you can talk to? Here in Australia the Salvation Army provides counselling that includes debt negotiation. At least half the debt is his.
The frugal living movement could have been designed for your situation. I know this because I've had real financial constraints over the last 3 years. I've learned many easy ways of drastically cutting expenses and getting back on track. I make my own cleaning and washing compounds, cut back on utilities, cook from scratch take lunch, etc.
The internet is your friend here, for looking up tips and doing simple DIY jobs yourself. Although your starting point seems impossible, start paying down debt like your life depended on it, and you will get there.