Collection action taken for Ex's debt what rights?

My husbands ex-wife has primary custody of his two boys. With that comes us paying child support which includes paying half the daycare cost. A couple of months back she decided to pull them out of the daycare they were attending (without the 30 days notice the daycare required due to an incident that occurred with one of the kids that left him feeling uncomfortable going back) and place them in a new daycare.

She apparently settled with them to pay $400 to get out of the contract at that time. A couple of days ago my husband got a letter from a collection agency with a $1400 bill from this daycare. When he called them he was informed his ex-wife had not paid the $400 she had said she would pay and now they were coming after us for the $400 bill, attorney fess and interest. Now my husband never signed the daycare contract, was not part of the settlement agreement she made and as he pays her each month for daycare has never had any ownership of that bill. Can the collection agency come after him for this amount and can it affect his credit?