You can scale the price to find a point where it's economical to offer to stay open while maintaining good relations and if the demand is consistent and heavy then scale that price appropriately or, alternatively, simply refuse to service repeat offenders if it's becoming a serious headache.

It's a bit of a hard question because the daycare may not have a legal way to stop holding the child, unlike fedex they can't simply return it to sender, so these sorts of contingencies might not be expected on opening your center, but you'll need to scale into them.