I understand. That's a lot of money to sink into a vehicle, but he has one of his own and with four kids you need it yourself. I assume that the kids are with you (but that's a separate issue).
So, he's going to expect you to take over the payments, and if you are going to keep the van then you should. At some point you and he need to go to TD to see if the loan can be transferred to your name. For that to happen, you'll need proof of income, including Child Tax Credit and child support from him.
Because there was no downpayment and because you just entered into this purchase, he has no "equity" in he van (other than payments towards it that he's made post separation if any), so the van issue isn't the biggest deal. The loan is in his name so he has incentive to see it paid because if it goes into default then it's his credit rating that gets hit. You have an incentive to see the loan payments made because if they aren't then the van is repossessed and your out of a vehicle with four kids.
So to answer your question, yes you owe him half of the value of the van. But half of nothing is still nothing. If he agrees to start paying the appropriate child support based on his income right away, then you can take over the van payments until everything else is sorted out.
Does that make sens Lindsey? Please reply if there is more to discuss. If I've answered you then I'd appreciate a positive service rating please.