Maybe something along the lines of,

We want a quiet, peaceful environment for the first few days when DD3 is born and while we would love to introduce DD3 to you all we would really appreciate it everyone could limit (maybe find a better word) their visits until we have all settled in as a family of 5 first.

I am a bit unsure about adding the bit about kids, would have to think more about that.

And you don't sound mean and grumpy at all