Do you really need this car? Be really honest with yourself - Is there any possibility you could manage with the van? I know it's not ideal but if you're really struggling you could get the car fixed, sell it to pay off what you owe and then save up for something more affordable - leaving you in less debt.
Do you have a good credit rating? 0% is quite difficult to get just now even though there appears to be millions of offers for 0% cards. It's only after the application that they offer you a rate.
Another thing you may have to look into is going back to work earlier than the 9 month period. If you can't afford to be off, you can't afford it. It's not worth the stress on you and your family. The happier the mum, the happier the baby. It sounds great being off for 9 months but sometimes it's just not an option - and your childcare is free so it's worth thinking about.
Try reviewing your household budget it might surprise you.
Registering your OH's business as a limited company would involve a lot more paperwork which might not be what you need right now. Plus you're liable for corporation tax on top of your own tax, as well as employers tax! Tax tax tax!
His tax bill as stated can come out in 3 installments - they don't really offer anything better than that I'm afraid
Have you sold your wedding dress/items? Might be worth getting them on ebay and making some money to pay the car bill if you want to keep it.
Check the servicing records as mentioned, if all is in order then I'm afraid you don't have much to go on, it's just one of these things unfortunately.