Very few parents have success using hitting (spanking, swatting, flicking, smacking) to stop hitting. It makes no logical sense to the child, and eventually kids comply out of pain or fear, but harbor the belief that when they are big and strong enough, they will be able to hit, too.
I don't understand who's who in your request. Is the 13mo your son or daughter? Is the 16mo your son or daughter? What's the nature of the trauma – the older child actually hitting the younger? Clarification would help.
With little to go on, I would simply have to suggest that the two children be kept apart as much as possible, perhaps with some physical barrier unless you are present to catch the hitting hand before it strikes. Both kids are too young for time outs to have much effect, but consistent, calm intervention, just stopping the action and separating the children, will at least prevent ongoing hurt.
Both of these children are too young to blame the behavior on a lack of playdates. What is probably most helpful is to be sure each has things to do that don't encroach on the other child's "territory." Kids this young play alongside each other rather than with each other.