There is no need to be livid, OP. He just did not understand what you meant by "nothing". To many people, "nothing" is something that needs to be filled up by activities, hence why he thought it would be OK if his mother could fill up that day. You just need to explain that "nothing" is actually a day to RECHARGE with just him and the kids and have a SLOW DAY, in which you will make plans as you go. No guest, even the most calm and unobtrusive one, because that takes away from the point of having as quiet a day as possible. Maybe he will understand that explanation better.
My husband would have made the same mistake, BTW. "Nothing" is a really hard concept for some people to understand!