This stress is not good for you or your baby. You have made it clear you are unable to provide care for this short time. You gave as much notice as possible. This client was completely out of line and very disrespectful to your situation.
Do not open the door should they arrive with their child.
Since you have a waiting list, why not refer to that to see if you can replace this family.
Taking 2 weeks off after having your baby? Are you sure you wouldn't need more time off? DCP in my area usually take at least a month, or just take one or two of their dck's until they feel up to taking on their whole crew again.
I wish you and your baby well