I would never dream of visiting someone with a new baby until at least day 2 or 3 unless they were immediate family. (or they had specifically asked me to)
I would never stop mum and dad and my ILs from visiting straight away but then again I have really understanding and thoughtful relatives!
Maybe use katy as an excuse, say that she needs the first day or whatever to bond with her new sibling and you need to spend time as a family until then. I always find visitors in hospital easier than at home though.
As for this week I would just say "sorry, too pg need to rest!"